Mastering Quadratic Equations: A CBSE Class 10 Maths Practice Quiz

Question 1

Which of the following is a quadratic equation?

Accepted Answer

$(x-2)^2 + 1 = 2x-3$

Answer

$x(x+1) + 8 = (x+2)(x-2)$

Answer

$x(x^2+1) = x^3 - 2x + 1$

Answer

$x^3 - 4x^2 + 2x + 1 = 0$

Question 2

The roots of the quadratic equation $x^2 - 9 = 0$ are:

Accepted Answer

$3, -3$

Answer

$9, 0$

Answer

$3, 0$

Answer

$-3, 0$

Question 3

If $x=1$ is a root of the equation $x^2 + kx + 3 = 0$, then the value of $k$ is:

Accepted Answer

$-4$

Answer

$4$

Answer

$-2$

Answer

$2$

Question 4

The standard form of a quadratic equation is:

Accepted Answer

$ax^2+bx+c=0$, where $a 
eq 0$

Answer

$ax+b=0$

Answer

$ax^3+bx^2+cx+d=0$

Answer

$ax^2+b=0$

Question 5

Find the roots of the equation $x^2 - 7x + 10 = 0$ by factorization.

Accepted Answer

$2, 5$

Answer

$-2, -5$

Answer

$2, -5$

Answer

$-2, 5$

Question 6

The discriminant of the quadratic equation $3x^2 - 2x + 1 = 0$ is:

Accepted Answer

$-8$

Answer

$16$

Answer

$4$

Answer

$-4$

Question 7

For what value of $k$ does the quadratic equation $kx^2 + 4x + 1 = 0$ have real and equal roots?

Accepted Answer

$k=4$

Answer

$k=-4$

Answer

$k=0$

Answer

$k=16$

Question 8

The sum of the roots of the quadratic equation $2x^2 - 5x + 3 = 0$ is:

Accepted Answer

$\frac{5}{2}$

Answer

$-\frac{5}{2}$

Answer

$\frac{3}{2}$

Answer

$-\frac{3}{2}$

Question 9

If the product of the roots of the equation $ax^2 - 6x - 6 = 0$ is $2$, then the value of $a$ is:

Accepted Answer

$-3$

Answer

$3$

Answer

$2$

Answer

$-2$

Question 10

Which of the following quadratic equations has roots $2$ and $3$?

Accepted Answer

$x^2 - 5x + 6 = 0$

Answer

$x^2 + 5x + 6 = 0$

Answer

$x^2 - 5x - 6 = 0$

Answer

$x^2 + 5x - 6 = 0$

Question 11

The roots of the quadratic equation $x^2 + x - 12 = 0$ are:

Accepted Answer

$3, -4$

Answer

$-3, 4$

Answer

$3, 4$

Answer

$-3, -4$

Question 12

If one root of the quadratic equation $2x^2 + kx - 6 = 0$ is $2$, then the other root is:

Accepted Answer

$-\frac{3}{2}$

Answer

$3$

Answer

$-3$

Answer

$\frac{3}{2}$

Question 13

A quadratic equation whose roots are $0$ and $-4$ is:

Accepted Answer

$x^2 + 4x = 0$

Answer

$x^2 - 4x = 0$

Answer

$x^2 + 4 = 0$

Answer

$x^2 - 4 = 0$

Question 14

The value of $k$ for which the quadratic equation $x^2 - 4x + k = 0$ has no real roots is:

Accepted Answer

$k > 4$

Answer

$k < 4$

Answer

$k = 4$

Answer

$k < 0$

Question 15

A rectangular park is to be designed whose breadth is $3m$ less than its length. Its area is to be $4$ square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12m$. What is the length of the rectangular park?

Accepted Answer

$7m$

Answer

$10m$

Answer

$12m$

Answer

$15m$

Question 16

The values of $x$ for which the equation $(x-2)(x+3) = 0$ is satisfied are:

Accepted Answer

$2, -3$

Answer

$2, 3$

Answer

$-2, 3$

Answer

$-2, -3$

Question 17

The quadratic equation whose roots are $2 + \sqrt{3}$ and $2 - \sqrt{3}$ is:

Accepted Answer

$x^2 - 4x + 1 = 0$

Answer

$x^2 + 4x + 1 = 0$

Answer

$x^2 - 4x - 1 = 0$

Answer

$x^2 + 4x - 1 = 0$

Question 18

What is the nature of the roots of the quadratic equation $2x^2 - 3x + 5 = 0$?

Accepted Answer

No real roots

Answer

Real and distinct

Answer

Real and equal

Answer

Cannot be determined

Question 19

If the roots of $ax^2 + bx + c = 0$ are reciprocal of each other, then:

Accepted Answer

$a=c$

Answer

$a=b$

Answer

$b=c$

Answer

$a=b=c$

Question 20

The roots of the equation $\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0$ are:

Accepted Answer

$-\sqrt{2}, -\frac{5}{\sqrt{2}}$

Answer

$\sqrt{2}, \frac{5}{\sqrt{2}}$

Answer

$\sqrt{2}, -\frac{5}{\sqrt{2}}$

Answer

$-\sqrt{2}, \frac{5}{\sqrt{2}}$

Question 21

If $x = -2$ is a solution of $x^2 + mx + 6 = 0$, then $m$ is:

Accepted Answer

$5$

Answer

$-5$

Answer

$1$

Answer

$-1$

Question 22

A natural number, when increased by $12$, equals $160$ times its reciprocal. Find the number.

Accepted Answer

$8$

Answer

$4$

Answer

$12$

Answer

$20$

Question 23

The values of $k$ for which the quadratic equation $3x^2 + kx + 3 = 0$ has real roots are:

Accepted Answer

$k \ge 6$ or $k \le -6$

Answer

$-6 < k < 6$

Answer

$k \ge 0$

Answer

$k \le 0$

Question 24

Using the quadratic formula, solve $x^2 - 3x - 10 = 0$.

Accepted Answer

$5, -2$

Answer

$-5, 2$

Answer

$10, -1$

Answer

$-10, 1$

Question 25

If $x = -1$ is a root of the equation $3x^2 + Px - 5 = 0$, then $P$ is:

Accepted Answer

$2$

Answer

$8$

Answer

$-2$

Answer

$-8$

Question 26

The equation $x^2 - 4x + k = 0$ has two distinct real roots if:

Accepted Answer

$k<4$

Answer

$k=4$

Answer

$k>4$

Answer

$k=0$

Question 27

The value of $\sqrt{6+\sqrt{6+\sqrt{6+...}}}$ is:

Accepted Answer

$3$

Answer

$4$

Answer

$2$

Answer

$1$

Question 28

If one root of the equation $x^2 - ax + 3 = 0$ is $1$, then the other root is:

Accepted Answer

$3$

Answer

$-3$

Answer

$2$

Answer

$-2$

Question 29

What will be the quadratic equation if its roots are $1/2$ and $-1/2$?

Accepted Answer

$4x^2 - 1 = 0$

Answer

$4x^2 + 1 = 0$

Answer

$x^2 - 1/4 = 0$

Answer

$x^2 + 1/4 = 0$

Question 30

A train travels $360$ km at a uniform speed. If the speed had been $5$ km/h more, it would have taken $1$ hour less for the same journey. Find the original speed of the train.

Accepted Answer

$40$ km/h

Answer

$30$ km/h

Answer

$35$ km/h

Answer

$45$ km/h

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Mastering Quadratic Equations: A CBSE Class 10 Maths Practice Quiz

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