Grade 10 : Mathematics - 4. Quadratic Equations (Set 2)

Question 1

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

Accepted Answer

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

Answer

A) $x^2 + \frac{2}{x} = 5$

Answer

C) $x^3 - 4x + 1 = 0$

Answer

D) $x + 3 = 0$

Question 2

What are the values of coefficients $a$, $b$, and $c$ when the equation $(x - 3)(x + 2) = 4$ is written in standard form $ax^2 + bx + c = 0$?

Accepted Answer

A) $a = 1, b = -1, c = -10$

Answer

B) $a = 1, b = -1, c = -6$

Answer

C) $a = 1, b = 1, c = -10$

Answer

D) $a = 1, b = -5, c = -6$

Question 3

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

Accepted Answer

B) $x = 3, 4$

Answer

A) $x = -3, -4$

Answer

C) $x = -3, 4$

Answer

D) $x = 3, -4$

Question 4

If $x = 2$ is a root of the quadratic equation $kx^2 + 2x - 8 = 0$, what is the value of $k$?

Accepted Answer

A) $k = 1$

Answer

B) $k = 2$

Answer

C) $k = -1$

Answer

D) $k = 4$

Question 5

What is the discriminant ($D = b^2 - 4ac$) of the quadratic equation $2x^2 - 5x + 3 = 0$?

Accepted Answer

A) 1

Answer

B) 25

Answer

C) 49

Answer

D) -1

Question 6

If the discriminant of a quadratic equation is zero ($D = 0$), what is the nature of its roots?

Accepted Answer

B) Two equal real roots

Answer

A) Two distinct real roots

Answer

C) No real roots

Answer

D) Infinite real roots

Question 7

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

Accepted Answer

B) $k = \pm 6$

Answer

A) $k = \pm 3$

Answer

C) $k = \pm 9$

Answer

D) $k = \pm 36$

Question 8

What is the sum of the roots of the quadratic equation $3x^2 - 12x + 5 = 0$?

Accepted Answer

B) 4

Answer

A) -4

Answer

C) $\frac{5}{3}$

Answer

D) $-\frac{5}{3}$

Question 9

What is the product of the roots of the quadratic equation $4x^2 + 8x - 12 = 0$?

Accepted Answer

C) -3

Answer

A) 2

Answer

B) -2

Answer

D) 3

Question 10

Which quadratic equation has 5 and -2 as its roots?

Accepted Answer

A) $x^2 - 3x - 10 = 0$

Answer

B) $x^2 + 3x - 10 = 0$

Answer

C) $x^2 - 3x + 10 = 0$

Answer

D) $x^2 + 7x - 10 = 0$

Question 11

According to the quadratic formula, what are the roots of $ax^2 + bx + c = 0$ ($a eq 0$)?

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 12

The area of a rectangular garden is $60m^2$. Its length is 7 m longer than its width $w$.

Which quadratic equation represents this situation in terms of width $w$?

Accepted Answer

B) $w^2 + 7w - 60 = 0$

Answer

A) $w^2 + 7w + 60 = 0$

Answer

C) $w^2 - 7w - 60 = 0$

Answer

D) $2w + 7 = 60$

Question 13

The product of two consecutive positive integers is 156. What is the smaller integer?

Accepted Answer

B) 12

Answer

A) 11

Answer

C) 13

Answer

D) 14

Question 14

Determine the nature of roots for the quadratic equation $x^2 + 2x + 5 = 0$.

Accepted Answer

C) No real roots

Answer

A) Two distinct real roots

Answer

B) Two equal real roots

Answer

D) Infinite real roots

Question 15

To solve $x^2 + 6x = 7$ by completing the square, what number must be added to both sides?

Accepted Answer

C) 9

Answer

A) 3

Answer

B) 6

Answer

D) 36

Question 16

Find the roots of $x^2 - 6x + 8 = 0$ using the quadratic formula.

Accepted Answer

A) $x = 2, 4$

Answer

B) $x = -2, -4$

Answer

C) $x = 1, 8$

Answer

D) $x = -1, -8$

Question 17

Rohan's mother is 26 years older than Rohan. The product of their ages 3 years from now will be 360. Rohan's present age is $x$ years.

Which quadratic equation models this problem?

Accepted Answer

A) $x^2 + 32x - 273 = 0$

Answer

B) $x^2 + 26x - 360 = 0$

Answer

C) $x^2 + 29x - 273 = 0$

Answer

D) $x^2 + 32x + 273 = 0$

Question 18

What are the roots of the equation $3x(2x - 5) = 0$?

Accepted Answer

A) $x = 0$ and $x = \frac{5}{2}$

Answer

B) $x = 3$ and $x = \frac{5}{2}$

Answer

C) $x = 0$ and $x = -\frac{5}{2}$

Answer

D) $x = 3$ and $x = -\frac{2}{5}$

Question 19

A right-angled triangle has base xcm and height $(x + 2)cm$.

If the area of the triangle is $24cm^2$, what is the value of $x$?

Accepted Answer

B) 6 cm

Answer

A) 4 cm

Answer

C) 8 cm

Answer

D) 10 cm

Question 20

Find the non-zero root of the equation $5x^2 - 20x = 0$.

Accepted Answer

B) 4

Answer

A) 2

Answer

C) 5

Answer

D) 20

Grade 10 : Mathematics - 4. Quadratic Equations (Set 2)