Sample QuestionsQuadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The discriminant of equation $5 x^2-6 x=1 ; b^2-4 a c=$ _______
- ✓
$16$
- B
$\sqrt{56}$
- C
$4$
- D
$56$
Answer: A.
View full solution →The discriminant is _______ of quadratic equation. $3 x^2-7 x+2=0$.
Answer: D.
View full solution →The equation of discriminant is _______ of quadratic equation $a x^2+b x+c=0$.
- A
$b^2+4 a c$
- ✓
$b^2-4 a c$
- C
$b^2-a c$
- D
$b-4 a c$
Answer: B.
View full solution →The Discriminant of quadratic Equation $2 x^2-3 x+5$ $=0$ is _______ .
Answer: B.
View full solution →The quadratic equation $a x^2-4 a x+2 a+1=0$ has repeated roots, if $a=$
Answer: B.
View full solution →If one root of the quadratic equation $2 x^2+5 x-3=0$ is $\frac{1}{2}$ then its other root is ....... $(3,-3, \pm 3)$
View full solution →Roots of the quadratic equation are equal then $b^2-4 a c=\ldots \ldots \ldots .(1,2,0)$
View full solution →If roots of the equation $x^2-k x+4=0$ are equal then $k=\ldots \ldots .(4,-4, \pm 4)$
View full solution →Find discriminant of sqquare root discriminent Area $\sqrt{5} x^2-7 x+2 \sqrt{5}=0 .(49,9,7)$
View full solution →Numbers at maximum zeroes at quadratic equation are ...... (one, three, two)
$(x+1)^2=2(x-3)$ is not a quadratic equation.
View full solution →The equation $x^2-5 x+6=0$ has distinct roots.
View full solution →The equation $x^2-10 x+25=0$ has distinct roots.
View full solution →State whether the following statement is true or false: The discriminant of the equation $x^2+8 x+21=0$ is -20 .
View full solution →A quadratic equation has at least two real roots.
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 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 →Find the nature of the roots of the quadratic equation $2x^2- 3x + 5 = 0$. If the real roots exist. Find it.
View full solution →Find two numbers whose sum is $27$ and product is $182$.
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).
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 →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 $48$.
View full solution →Find the value of $k$ for the quadratic equation $kx(x − 2) + 6 = 0$, so that they have two equal roots.
View full solution →Find the value of k for the quadratic equation $2 x^2+k x+3=0$, so that they have two real equal roots.
View full solution →Find the nature of the roots of the quadratic equation $2 x^2-6 x+3=0$. If the real roots exist. Find it.
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 →| A | B |
| Q.1. Which quadratic equationhas equal roots ? | (a) 2 |
| Q.2. The roots of the equation $25 x^2-x(m-2)-1=0$ are additive inverse of each other then $m=\ldots \ldots$ | (b) $x^2-12 x+36=0$ |
| | (c)-2 |
| A | B |
| Q.1. …….. equation has one solution in R. | (a) 15 |
| Q.2. .......is the discriminant of a quadratic equation $5 x^2-6 x+1=0$ | (b) $x^2+10 x+25=0$ |
| | (c) 16 |
| A | B |
| Q.1. Write the solution of $x^2-3 x-10=0$ | (a) x = 5 x = - 2 |
| Q.2. If……… then the quadratic equation has no real roots. | (b) x = - 5 x = 2 |
| | (c) Discriminant D < 0 |
| A | B |
| Q.1. Which is not a quadratic equation? | (a) $(x-2)^2+1=2 x-3$ |
| Q.2. Which is a quadratic equation? | (b) $x^{-2}+8 x+15$ |
| | (c) $x(x+1)+8=(x+2)(x-2)$ |
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 →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 →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 $48.$
View full solution →Find the value of $k$ for the quadratic equation $kx(x − 2) + 6 = 0,$ so that they have two equal roots.
View full solution →A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If, the total cost of production on that day was ₹ 90, find the number of articles produced and the cost of each article.