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This mock test of Test: Quadratic Equations - 3 for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Test: Quadratic Equations - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which of the following quadratic expression can be expressed as a product of real linear factors?

Solution:

Thus, it can be expressed as product of linear factors.

QUESTION: 2

Two candidates attempt to solve a quadratic equation of the form x^{2} + px + q = 0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :

Solution:

QUESTION: 3

Solve for x : 15x^{2} – 7x – 36 = 0

Solution:

QUESTION: 4

Solve for y : (√7) y^{2} – 6y –13 (√7) = 0

Solution:

Using mid term splitting

So either y=13/

Or y=

QUESTION: 5

Solve for x : 6x^{2} + 40 = 31x

Solution:

QUESTION: 6

Determine k such that the quadratic equation x^{2} + 7(3 + 2k) – 2x (1 + 3k) = 0 has equal roots :

Solution:

QUESTION: 7

Discriminant of the equation – 3x^{2} + 2x – 8 = 0 is

Solution:

QUESTION: 8

The nature of the roots of the equation x^{2} – 5x + 7 = 0 is –

Solution:

Given equation is x^{2}-5x+7=0

We have discriminant as b^{2}-4ac=(-5)^{2}-4*1*7= -3

And x = , Since we do not have any real number which is a root of a negative number, the roots are not real.

QUESTION: 9

The roots of a^{2}x^{2} + abx = b^{2}, a = 0 are :

Solution:

QUESTION: 10

The equation x^{2} – px + q = 0 p, q ε R has no real roots if :

Solution:

QUESTION: 11

Determine the value of k for which the quadratic equation 4x^{2} – 3kx + 1 = 0 has equal roots :

Solution:

QUESTION: 12

Find the value of k such that the sum of the squares of the roots of the quadratic equation x^{2} – 8x + k = 0 is 40:

Solution:

QUESTION: 13

Find the value of p for which the quadratic equation x^{2} + p(4x + p – 1) + 2 = 0 has equal roots :

Solution:

QUESTION: 14

The length of a hypotenuse of a right triangle exceeds the length of its base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle (in cm) :

Solution:

QUESTION: 15

A two digit number is such that the product of it's digits is 12. When 9 is added to the number, the digits interchange their places, find the number :

Solution:

QUESTION: 16

A plane left 40 minutes late due to bad weather and in order to reach it's destination, 1600 km away in time,it had to increase it's speed by 400 km/h from it's usual speed. Find the usual speed of the plane :

Solution:

QUESTION: 17

The sum of the squares of two consecutive positive odd numbers is 290. Find the sum of the numbers :

Solution:

QUESTION: 18

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount, each book would have cost Re. 1 less. How many books did he buy?

Solution:

QUESTION: 19

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm^{2}. Find the sides of the square.

Solution:

QUESTION: 20

The real values of a for which the quadratic equation 2x^{2} – (a^{3} + 8a – 1) x + a^{2} – 4a = 0 possesses roots of opposite signs are given by :

Solution:

QUESTION: 21

The number of real solutions of the equation is :

Solution:

QUESTION: 22

If the equation (3x)^{2} + (27 × 3^{1/k }– 15) x + 4 = 0 has equal roots, then k =

Solution:

QUESTION: 23

If x =

Solution:

QUESTION: 24

Equation ax^{2} + 2x + 1 has one double root if :

Solution:

QUESTION: 25

Solve for x : (x + 2) (x – 5) (x – 6) (x + 1) = 144 :

Solution:

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