Grade 10 : Mathematics - 4. Quadratic Equations (Set 1)

Question 1

Which of the following equations represents a quadratic equation in variable $x$?

Accepted Answer

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

Answer

A) $2x + 5 = 0$

Answer

C) $x^3 - 2x^2 + x = 0$

Answer

D) $\frac{1}{x} + x = 2$

Question 2

What is the value of the discriminant ($D$) for the quadratic equation $x^2 + 5x + 6 = 0$?

Accepted Answer

A) 1

Answer

B) 0

Answer

C) 25

Answer

D) 49

Question 3

What are the roots of the quadratic equation $x^2 - 9 = 0$?

Accepted Answer

C) $x = 3$ and $x = -3$

Answer

A) $x = 3$ only

Answer

B) $x = -3$ only

Answer

D) $x = 9$ and $x = -9$

Question 4

What is the sum of the roots of the quadratic equation $x^2 - 7x + 12 = 0$?

Accepted Answer

B) 7

Answer

A) -7

Answer

C) 12

Answer

D) -12

Question 5

What is the product of the roots of the quadratic equation $2x^2 + 8x + 6 = 0$?

Accepted Answer

A) 3

Answer

B) 6

Answer

C) 4

Answer

D) -4

Question 6

If one root of the quadratic equation $x^2 - 5x + k = 0$ is 2, what is the value of $k$?

Accepted Answer

C) 6

Answer

A) 5

Answer

B) -6

Answer

D) 10

Question 7

What is the nature of the roots of a quadratic equation if its discriminant $D = 0$?

Accepted Answer

B) Two equal real roots

Answer

A) Two distinct real roots

Answer

C) No real roots

Answer

D) Three real roots

Question 8

Solve the quadratic equation $x^2 + 6x + 8 = 0$ by factorisation.

Accepted Answer

B) $x = -2, -4$

Answer

A) $x = 2, 4$

Answer

C) $x = -2, 4$

Answer

D) $x = 2, -4$

Question 9

Which expression represents the standard quadratic formula for $ax^2 + bx + c = 0$?

Accepted Answer

A) $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Answer

B) $x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$

Answer

C) $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$

Answer

D) $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{a}$

Question 10

Calculate the discriminant of $2x^2 - 4x + 3 = 0$.

Accepted Answer

B) -8

Answer

A) 8

Answer

C) 40

Answer

D) -40

Question 11

Construct the quadratic equation whose roots are 3 and 4.

Accepted Answer

B) $x^2 - 7x + 12 = 0$

Answer

A) $x^2 + 7x + 12 = 0$

Answer

C) $x^2 - 12x + 7 = 0$

Answer

D) $x^2 + 7x - 12 = 0$

Question 12

If the discriminant of a quadratic equation is negative ($D < 0$), what can be concluded about its roots?

Accepted Answer

C) There are no real roots

Answer

A) The roots are real and equal

Answer

B) The roots are real and distinct

Answer

D) The roots are always positive integers

Question 13

Solve the equation $(x - 3)^2 = 25$.

Accepted Answer

A) $x = 8, -2$

Answer

B) $x = 8, 2$

Answer

C) $x = -8, 2$

Answer

D) $x = 5, -5$

Question 14

For what values of $k$ does the quadratic equation $x^2 - kx + 9 = 0$ have real and equal roots?

Accepted Answer

B) $k = \pm 6$

Answer

A) $k = 3$ only

Answer

C) $k = 9$ only

Answer

D) $k = \pm 3$

Question 15

The length of a rectangular garden is 2 m longer than its width $x$. The total area of the garden is $15m^2$.

Which quadratic equation represents this situation?

Accepted Answer

C) $x^2 + 2x - 15 = 0$

Answer

A) $x^2 + 2x + 15 = 0$

Answer

B) $x^2 - 2x - 15 = 0$

Answer

D) $2x^2 + x - 15 = 0$

Question 16

Find the positive root of the quadratic equation $x^2 - 3x - 10 = 0$.

Accepted Answer

C) 5

Answer

A) 2

Answer

B) 3

Answer

D) 10

Question 17

Solve the quadratic equation $3x^2 - 12 = 0$.

Accepted Answer

B) $x = \pm 2$

Answer

A) $x = 2$ only

Answer

C) $x = 4$ only

Answer

D) $x = \pm 4$

Question 18

What is the degree of a quadratic polynomial?

Accepted Answer

B) 2

Answer

A) 1

Answer

C) 3

Answer

D) 0

Question 19

If the roots of $x^2 - px + q = 0$ are 1 and 5, what are the values of $p$ and $q$?

Accepted Answer

A) $p = 6, q = 5$

Answer

B) $p = -6, q = 5$

Answer

C) $p = 5, q = 6$

Answer

D) $p = 6, q = -5$

Question 20

What is the discriminant of the quadratic equation $x^2 - 4x + 4 = 0$?

Accepted Answer

C) 0

Answer

A) 16

Answer

B) 8

Answer

D) -16

Grade 10 : Mathematics - 4. Quadratic Equations (Set 1)