The roots of the quadratic equation $2x^2- x - 6 = 0$ are :
- A$-2,\frac{3}{2}$
- ✓$2,\frac{-3}{2}$
- C$-2,\frac{-3}{2}$
- D$2,\frac{3}{2}$
Answer: B.
View full solution →Question types
Quadratic Equations question types
295 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
295
Questions
7
Question groups
5
Question types
01
M.C.Q (1 Marks)
203 Q→02Assertion (A) & Reason (B) MCQ
38 Q→03True False[1 Marks ]
6 Q→041 Marks Question
23 Q→052 Marks Questions
17 Q→063 Marks Question
3 Q→07Case study (4 Marks)
5 Q→Sample Questions
Quadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The roots of the equation $x^2- 3x - m(m + 3) = 0,$ where $m$ is a constant, are :
- A$m, m + 3$
- ✓$-m, m + 3$
- C$m, -(m + 3)$
- D$-m, -(m: 3)$
Answer: B.
View full solution →If $1$ is a root of the equations $ay^2+ ay + 3 = 0$ and $y^2+ y + b = 0$, then $ab$ equals :
- ✓$3$
- B$-\frac{7}{2}$
- C$6$
- D$-3$
Answer: A.
View full solution →The roots of the equation $x^2+ x - p(p + 1) = 0$, where $p$ is a constant, are :
- A$p, p + 1$
- B$-p, p + 1$
- ✓$p, - (p + 1)$
- D$−p, - (p + 1)$
Answer: C.
View full solution →The value $(s)$ of $k$ for which the quadratic equation $2x^2+ kx + 2 = 0$ has equal roots, is :
- A$4$
- ✓$\pm4$
- C$-4$
- D$0$
Answer: B.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $(2 x-1)^2-4 x^2+5=0$ is not a quadratic equation.
Reason : An equation of the form $a x^2+b x+c=0, a \neq 0$, where $a, b, c \in R$ is called a quadratic equation.
Assertion : $(2 x-1)^2-4 x^2+5=0$ is not a quadratic equation.
Reason : An equation of the form $a x^2+b x+c=0, a \neq 0$, where $a, b, c \in R$ is called a quadratic equation.
- AIf both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
- ✓If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
- CIf Assertion is correct but Reason is incorrect.
- DIf Assertion is incorrect but Reason is correct.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A) : (2 x-1)^2-4 x^2+5=0$ ota quadratic equation.
Reason $(R) : x=0,3$ are the roots of the equation $2 x^2-6 x=0$.
Assertion $(A) : (2 x-1)^2-4 x^2+5=0$ ota quadratic equation.
Reason $(R) : x=0,3$ are the roots of the equation $2 x^2-6 x=0$.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
- ✓Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$ .
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true
Answer: B.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R$) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $3 y^2+17 y-30=0$ have distinct roots.
Reason : The quadratic equation $a x^2+b x+c=0$ have distinct roots $($real roots$)$ if $D>0$.
Assertion : $3 y^2+17 y-30=0$ have distinct roots.
Reason : The quadratic equation $a x^2+b x+c=0$ have distinct roots $($real roots$)$ if $D>0$.
- ✓Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : A quadratic equation $ax^2 + bx + c = 0$, has two distinct real roots, if $b^2 - 4ac > 0$.
Reason : A quadratic equation can never be solved by using method of completing the squares.
Assertion : A quadratic equation $ax^2 + bx + c = 0$, has two distinct real roots, if $b^2 - 4ac > 0$.
Reason : A quadratic equation can never be solved by using method of completing the squares.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A).$
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓Assertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true
Answer: C.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : $2\sqrt{2}$ is a root of the quadratic equation $\text{x}2−4\sqrt{2}\text{x}+8=0.$
Reason : The root of a quadratic equation satisfies it.
Assertion : $2\sqrt{2}$ is a root of the quadratic equation $\text{x}2−4\sqrt{2}\text{x}+8=0.$
Reason : The root of a quadratic equation satisfies it.
- ✓If both assertion and reason are true and reason is the correct explanation of assertion.
- BIf both assertion and reason are true but reason is not the correct explanation of assertion.
- CIf assertion is true but reason is false.
- DIf both assertion and reason are false.
Answer: A.
View full solution →Write whether the following statements are true or false. Justify your answers.
Every quadratic equations has at most two roots.
Every quadratic equations has at most two roots.
Write whether the following statements are true or false. Justify your answers.
Every quadratic equation has at least one real root.
Every quadratic equation has at least one real root.
Write whether the following statements are true or false. Justify your answers.
If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
View full solution →If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Write whether the following statements are true or false. Justify your answers.
If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
View full solution →If the coefficient of $x^2$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Write whether the following statements are true or false. Justify your answers.
Every quadratic equation has at least two roots.
Every quadratic equation has at least two roots.
Find the nature of the roots of the quadratic equation $2 x^2-3 x+5=0$. If the real roots exist. Find it.
View full solution →John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. Represent situation mathematically (quadratic equation).
Find the roots of the quadratic equation $100x^2- 20x + 1 = 0$ by factorization.
View full solution →Find the roots of the quadratic equation $2x^2-x+{1 \over8} = 0$ by factorization.
View full solution →Find the roots of the quadratic equation $\sqrt { 2 } x ^ { 2 } + 7 x + 5 \sqrt { 2 } = 0$ by factorization.
View full solution →Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m$^2$? If so, find its length and breadth.
View full solution →Find the value of k for the quadratic equation kx(x − 2) + 6 = 0, so that they have two equal roots.
Find the value of k for the quadratic equation $2 x ^2+ kx +3=0$, so that they have two real equal roots.
View full solution →Find the nature of the roots of the quadratic equation $3 x ^ { 2 } - 4 \sqrt { 3 } x + 4 = 0$. If the real roots exist. Find it.
View full solution →Is it possible to design a rectangular park of perimeter $80 \ m$ and area $400 \ m^2$? If so, find its length and breadth.
View full solution →A pole has to be erected at a point on the boundary of a circular park of diameter $13$ metres in such a way that the difference of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7$ metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?
View full solution →Find the roots of equation:$\frac { 1 } { x } - \frac { 1 } { ( x - 2 ) } = 3 , x \neq 0,2$
View full solution →Applications of Parabola - Suspension Bridge
If the road the roadway of a suspension bridge is loaded uniformly par horizontal meter, the suspension cable hangs in the form of arc which closely approximate to parabolic arcs. Therefore, parabolic arcs are used in suspension cable bridge construction.
Parabola: A parabola is the graph that results from $px(x) = ax^2 + bx + c$. Parabola are symmetric about a vertical line known as the Axis of symmetry.
- Find the number of polynomial having zeroes as 1 and -2.
- Graph of quadratic polynomial is a:
- If the susnension cable of a bridge hangs in the form of arcs is represented by $4x^2- 20x + 9,$ then its zerores are:
Or
The number of zeroes that polynomial $p(x) = x^3 - 4x$ can have is:
Applications of Parabolas-Highway Overpasses/ Underpasses A highway underpass is parabolic in shape.
Parabola: A parabola is the graph that results from $p(x) = ax^2 + bx + c$ Parabolas are symmetric about a vertical line known as the Axis of Symmetry. The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the vertex.
- The highway overpass is represented graphically. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial:
- Graph of a quadratic polynomial is a:
- The representation of Highway Underpass whose one zero is 10 and sum of the zeroes is 16, is:
Or
The number of zeroes that polynomial $f(x) = (x - 3)^2 + 1$ can have is:
Applications of Parabolas
Parabola has many applications in our day-to-day life. For example, if an object (projectile) is thrown in space, then the path of the projectile is a parabola. If we know the equation of the path of a projectile by using various properties of parabola, we can obtain may important results like greatest height attained by the projectile, its horizontal range reached etc.
Parabola: A parabola is the graph that results from $p(x) = ax^2 + bx + c$ they are symmetric about a vertical line known as the axis of symmetry and runs through the maximum or minimum point of the parabola which is called the vertex.
Graph of a quadratic polynomial is:
The number of zeroes that polynomial $p(x)=(x-2)^2+5$ can have is:
If a parabolic trajectory is represented by $x^2-4 x+3$, then its zeroes are:
Or
If one zero of a parabolic trajectory $p(y)=5 y^2-14 y+k$ is reciprocal of the other, the find the value of $k$ :
A highway underpass a parabolic in shape
Parabola: A parabola is the graph that results from $p(x) = ax^2 + bx + c$. Parabolas are symmetric about a vertical line known as the axis of symmetry.
- Graph of a quadratic polynomial is ?
- The highway overpass is represented graphically. Zeroes of the polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of the polynomial ?
- If the highway overpass is represented by $x^2 + 2x - 15,$ then its zeroes are ?
Or
The number of zeroes for the polynomial $\text{y} = \text{g(x)} = (\text{x} + 3) (\text{x} - 1) - 3\Big(\text{x}-\frac13\Big)$ is ?
Applications of Parabola - Suspension Bridge
If the road the roadway of a suspension bridge is loaded uniformly par horizontal meter, the suspension cable hangs in the form of arc which closely approximate to parabolic arcs. Therefore, parabolic arcs are used in suspension cable bridge construction.
Parabola: A parabola is the graph that results from $px(x) = ax^2 + bx + c$. Parabola are symmetric about a vertical line known as the Axis of symmetry.
- Find the number of polynomials having zeroes as 0 and -3:
- Graph of a quadratic polynomial is a:
- If the suspension cable of a bridge hangs in the form of arcs is represented by $x^2 - 9x + 8$, then its zeroes are:
Or
Find a quadratic polynomials whose are 2 and 5:
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