Choose the correct answer for the following question.
One of the roots of equation $x^2+m x-5=0$ is $2$; find m.
One of the roots of equation $x^2+m x-5=0$ is $2$; find m.
- A$-2$
- B$-\frac{1}{2}$
- ✓$\frac{1}{2}$
- D$2$
Answer: C.
View full solution →Question types
P-1 Quadratic Equations question types
410 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
410
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
46 Q→02Complete the following activities and rewrite it : (2M)
9 Q→032 Marks Questions
141 Q→04Complete the following activities and rewrite it ( 3 marks)
7 Q→053 Marks Question
62 Q→064 Marks Questions
85 Q→071 Marks Question
50 Q→08Solve the following sub questions( 3 Marks ):
10 Q→Sample Questions
P-1 Quadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Choose the correct answer for the following question.
$\sqrt{5} m^2-\sqrt{5} m+\sqrt{5}=0$ which of the following statement is true for this given equation?
$\sqrt{5} m^2-\sqrt{5} m+\sqrt{5}=0$ which of the following statement is true for this given equation?
- AReal and uneual roots
- BReal and equal roots
- ✓Roots are not real
- DThree roots.
Answer: C.
View full solution →Choose the correct answer for the following question.
Out of the following equations, find the equation having the sum of its roots -5.
A. $3 x^2-15 x+3=0$
B. $x^2-5 x+3=0$
C. $x^2+3 x-5=0$
D. $3 x^2+15 x+3=0$
View full solution →Out of the following equations, find the equation having the sum of its roots -5.
A. $3 x^2-15 x+3=0$
B. $x^2-5 x+3=0$
C. $x^2+3 x-5=0$
D. $3 x^2+15 x+3=0$
Choose the correct answer for the following question.
Which of the following quadratic equations has roots 3, 5?
A. $x^2-15 x+8=0$
B. $x^2-8 x+15=0$
C. $x^2+3 x+5=0$
D. $x^2+8 x-15=0$
View full solution →Which of the following quadratic equations has roots 3, 5?
A. $x^2-15 x+8=0$
B. $x^2-8 x+15=0$
C. $x^2+3 x+5=0$
D. $x^2+8 x-15=0$
Choose the correct answer for the following question.
For $\sqrt{2} x^2+5 x+\sqrt{2}=0$ find the value of the discriminant.
For $\sqrt{2} x^2+5 x+\sqrt{2}=0$ find the value of the discriminant.
- A$-5$
- ✓$17$
- C$2$
- D$2 \sqrt{2}-5$
Answer: B.
View full solution →If α, β are roots of quadratic equation,
What will be the quadratic equation if $\alpha=2, \beta=5$.
$x^2-(\alpha+\beta) x+(\alpha \beta)=0$
∴ $x^2$ -( ⬜ + ⬜) x + ⬜ $\times$ ⬜ = 0
∴ ⬜$x^2$ - ⬜x + ⬜ = 0
View full solution →$x^2-(\alpha+\beta) x+(\alpha \beta)=0$
∴ $x^2$ -( ⬜ + ⬜) x + ⬜ $\times$ ⬜ = 0
∴ ⬜$x^2$ - ⬜x + ⬜ = 0
Fill in the empty boxes properly.
$10 x^2+10 x+1=0$
Comparing the above equation with
$a x^2+b x+c=0$, we get
a = 10, b = 10, c = 1
∴$\alpha+\beta=$ ⬜
∴ and $\alpha \times \beta$ = ⬜
View full solution →$10 x^2+10 x+1=0$
Comparing the above equation with
$a x^2+b x+c=0$, we get
a = 10, b = 10, c = 1
∴$\alpha+\beta=$ ⬜
∴ and $\alpha \times \beta$ = ⬜
$2-\sqrt{5},2+\sqrt{5}$
View full solution →$\frac{1}{2},-\frac{1}{2}$
View full solution →3 and -10
0 and 4
Determine the nature of roots of the following quadratic equation.
$m^2+2 m+9=0$
View full solution →$m^2+2 m+9=0$
If $\alpha$ and $\beta$ are the roots of $x^2+5 x-1=0$ then find :
1. $\alpha^3+\beta^3$
2. $\alpha^2+\beta^2$.
View full solution →1. $\alpha^3+\beta^3$
2. $\alpha^2+\beta^2$.
Decide which of the following are quadratic equations?
1. $3 x^2-5 x+3=0$
2. $9 y^2+5=0$
3. $m^3-5 m^2+4=0$
4. $(1+2)(1-5)=0$
Solution :
Solution:
1.In the equation $3 x^2-5 x+3=0, x$ is the only variable and maximum
index of the variable is 2
It is a quadratic equation.
2. In the equation $9 y^2+5=0$,
is the only variable and maximum index of the variable is
it a quadratic equation.
3.In the equation $m ^3-5 m^2+4=0$, is the only variable but maximum index of the variable is not $2.$
It quadratic equation.
$4((\mid+2)(\mid-5)=0$
$1(1-5)+2(\mid-5)=0$
$I^2-5|+2|-10=0$
$I^2-3 \mid-10=0$, In this equation. is the only variable and maximum index of the variable is
it a quadratic equation.
View full solution →1. $3 x^2-5 x+3=0$
2. $9 y^2+5=0$
3. $m^3-5 m^2+4=0$
4. $(1+2)(1-5)=0$
Solution :
Solution:
1.In the equation $3 x^2-5 x+3=0, x$ is the only variable and maximum
index of the variable is 2
It is a quadratic equation.
2. In the equation $9 y^2+5=0$,
is the only variable and maximum index of the variable isit
a quadratic equation.3.In the equation $m ^3-5 m^2+4=0$,
is the only variable but maximum index of the variable is not $2.$It
quadratic equation.$4((\mid+2)(\mid-5)=0$
$1(1-5)+2(\mid-5)=0$
$I^2-5|+2|-10=0$
$I^2-3 \mid-10=0$, In this equation.
is the only variable and maximum index of the variable isit
a quadratic equation.If $x=5$ is a root of equation $\mathrm{kx}^2-14 \mathrm{x}-5=0$, then find the value of $\mathrm{k}$ by completing the following activity.
One of the roots of equation $k x^2-14 x-5=0$ is $\square$.
$\therefore$ Now Let $x=\square$ in the equation.
$ k \square^2-14 \square-5=0$
$\therefore \quad 25 k-70-5=0$
$25 k-\square=0$
$25 k=\square$
$\therefore k=\frac{\square}{\square}=3 $
View full solution →One of the roots of equation $k x^2-14 x-5=0$ is $\square$.
$\therefore$ Now Let $x=\square$ in the equation.
$ k \square^2-14 \square-5=0$
$\therefore \quad 25 k-70-5=0$
$25 k-\square=0$
$25 k=\square$
$\therefore k=\frac{\square}{\square}=3 $
In the adjoining fig. ⬜ABCD is a trapezium AB||CD and its area is 33 cm2. From the information given in the figure find the lengths of all sides of the ⬜ABCD. Fill in the empty boxes to get the solution.
⬜ $\square ABCD$ is a trapezium. $AB \| CD$
Area of trapezium
$=\frac{1}{2} \times($ Sum of parallel sides $) \times$ Height
$\therefore \quad A (⬜ABCD )=\frac{1}{2} \times( AB + CD ) \times$⬜
$\therefore \quad 33=\frac{1}{2}(x+2 x+1) \times$⬜
∴ ⬜$=(3 x+1) \times$ ⬜
$\therefore \quad 66=3 x^2-12 x+x-4$
$\therefore \quad 3 x^2$ - ⬜ - ⬜ = 0
$\therefore \quad 3 x^2-21 x+10 x-70=0$
$\therefore \quad 3 x(x-7)+10(x-7)=0$
$\therefore \quad(3 x+10)(x-7)=0$
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
$\therefore \quad(3 x+10)=0$ or ⬜ = 0
$\therefore \quad x=\frac{-10}{3}$ or $x=$ ⬜
But, length is never nagative.
∴ $x \neq \frac{-10}{3}$
∴ x = ⬜
AB = ⬜
CD = ⬜
AD = BC = ⬜
View full solution →⬜ $\square ABCD$ is a trapezium. $AB \| CD$
Area of trapezium
$=\frac{1}{2} \times($ Sum of parallel sides $) \times$ Height
$\therefore \quad A (⬜ABCD )=\frac{1}{2} \times( AB + CD ) \times$⬜
$\therefore \quad 33=\frac{1}{2}(x+2 x+1) \times$⬜
∴ ⬜$=(3 x+1) \times$ ⬜
$\therefore \quad 66=3 x^2-12 x+x-4$
$\therefore \quad 3 x^2$ - ⬜ - ⬜ = 0
$\therefore \quad 3 x^2-21 x+10 x-70=0$
$\therefore \quad 3 x(x-7)+10(x-7)=0$
$\therefore \quad(3 x+10)(x-7)=0$
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
$\therefore \quad(3 x+10)=0$ or ⬜ = 0
$\therefore \quad x=\frac{-10}{3}$ or $x=$ ⬜
But, length is never nagative.
∴ $x \neq \frac{-10}{3}$
∴ x = ⬜
AB = ⬜
CD = ⬜
AD = BC = ⬜
One of the roots of equation 5m2 + 2m + k = 0 is $\frac{-7}{5}$ Complete the following activity to find the value of 'k'.
$[-]$ is a root of quadratic equation $5 m^2+2 m+k=0$
∴ Put m $[-]$ in the equation.
∴ 5 $ \times$ $[-]$ + 2 $\times$$[-]$ + k = 0
∴ $[-]$ + $[-]$ + k = 0
∴ ⬜ + k = 0
∴ k = ⬜
View full solution →$[-]$ is a root of quadratic equation $5 m^2+2 m+k=0$
∴ Put m $[-]$ in the equation.
∴ 5 $ \times$ $[-]$ + 2 $\times$$[-]$ + k = 0
∴ $[-]$ + $[-]$ + k = 0
∴ ⬜ + k = 0
∴ k = ⬜
The roots of each of the following quadratic equation are real and equal, find k.
kx (x-2) + 6 = 0
kx (x-2) + 6 = 0
The roots of each of the following quadratic equation are real and equal, find k.
$3 y^2+k y+12=0$
View full solution →$3 y^2+k y+12=0$
$\alpha^3+\beta^3$
View full solution →$\alpha^2+\beta^2$
View full solution →With the help of the flow chart given below solve the equation $x^2+2 \sqrt{3} x+3=0$ using the formula.
View full solution →If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and diviser.
Pintu takes 6 days more than those of Nishu to complete certain work. If they work together they finish it in 4 days. How many days would it take to complete the work if they work alone.
Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
Mr. Kasam runs a small business of making earthen pots. He makes certain number of pots on daily basis. Production cost of each pot is ₹40 more than 10 times total number of pots, he makes in one day. If production cost of all pots per day is ` 600, find production cost of one pot and number of pots he makes per day.
Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
$(x + 2)^2 = 2x^2$
View full solution →$x^2-2 x+5=x^2$
View full solution →$x^2+2 x+11=0$
View full solution →$y^2=7 y$
View full solution →$2 m^2=5 m-5$
View full solution →One of the roots of equation $5 m^2+2 m+k=0$ is $\frac{-7}{5}.$ Complete the following activity to find the value of 'k'.
View full solution →There is a rectangular onion storehouse in the farm of Mr. Ratnakarrao at Tivasa. The length of rectangular base is more than its breadth by 7 m and diagonal is more than length by 1 m. Find length and breadth of the storehouse.
The difference between the roots of the equation $x^2-13 x+\mathrm{k}=0$ is 7 find $\mathrm{k}$.
View full solution →Solve : x² + x + 5 = 0
Solve : 25x² + 30x + 9 = 0
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