IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 4

HARD

10th Foundation

IMPORTANT

Earn 100

If the roots of the equation $(a - b {) x}^{2} + (b - c) x + (c - a) = 0$ are equal. Then _____.

70% studentsanswered this correctly

Important Questions on Quadratic Equations

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 5

One of the two students, while solving a quadratic equation in

x

, copied the constant term incorrectly and got the roots

3

and

2

.The other copied the constant term and coefficient of

x^{2}

correctly as

- 6

and

1

respectively. The correct roots are _____.

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 6

If one of the roots of

2 x^{2} + ax + 32 = 0

is twice the other root, then the value of

a

is ______.

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 7

For what value of

a

, the roots of the equation

2 x^{2} + 6 x + a = 0

, satisfy the condition

(\frac{α}{β}) + (\frac{β}{α}) < 2

(where

α

and

β

are the roots of equation).

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 8

Roots of the quadratic equation

x^{2} + x - (a + 1) (a + 2) = 0

are _______.

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 9

The roots of the equation

3 \sqrt{x} + 5 ({x)}^{- \frac{1}{2}} = \sqrt{2}

can be found by solving,

HARD

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 10

If the roots of the equation

(a^{2} + b^{2}) x^{2} - 2 b (a + c) x + (b^{2} + c^{2}) = 0

are equal, then ______.

MEDIUM

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 11

Two numbers whose sum is

12

and the absolute value of whose difference is

4

are the roots of the equation _______.

MEDIUM

10th Foundation

IMPORTANT

IMO Olympiad Work Book 10>Chapter 4 - Quadratic Equations>MATHEMATICAL REASONING>Q 12

The roots of the equation

x^{2 / 3} + x^{1 / 3} - 2 = 0

are ______.