Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 31

EASY

NDA & NA EE

IMPORTANT

Earn 100

If the sum of the roots of the equation $a x^{2} + b x + c = 0$ is equal to the sum of their squares, then

50% studentsanswered this correctly

Important Questions on Theory of Equation

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 32

If

\cos α

and

\cos β (0 < α < β < π)

are the roots of the quadratic equation

4 x^{2} - 3 = 0,

then what is the value of

\sec α \times \sec β ?

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 33

Let

f (x)

be a quadratic expression such that

f (- 1) + f (2) = 0

. If one root of

f (x) = 0

is

3,

then the other root of

f (x) = 0

lies in:

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 34

If

x, y

are positive real numbers satisfying the system of equations

x^{2} + y \sqrt{x y} = 336, y^{2} + x \sqrt{x y} = 112,

then

x + y

equals

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 35

In a class, the total numbers of boys and girls are in the ratio

4 : 3

. On one day it was found that

8

boys and

14

girls were absent from the class and that the number of boys was the square of the number of girls. What is the total number of students in the class?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 36

The number of real solutions of

x - \frac{1}{x^{2} - 4} = 2 - \frac{1}{x^{2} - 4}

is

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 37

If

α, β

are the roots the quadratic equation

x^{2} - (3 + 2^{\sqrt{\log_{2} 3}} - 3^{\sqrt{\log_{3} 2}}) x - 2 (3^{\log_{3} 2} - 2^{\log_{2} 3}) = 0,

then the value of

α^{2} - α β + β^{2}

is equal to

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 38

If

α, β

be the roots of the equation

2 x^{2} - 35 x + 2 = 0,

then the value of

{(2 α - 35)}^{3} {(2 β - 35)}^{3}

is equal to

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 4 - Theory of Equation>Exercise 1>Q 39

If

α, β

are the roots of quadratic equation

x^{2} + p x + q = 0

and

γ, δ

are the roots of

x^{2} + p x - r = 0

, then

(α - γ) \cdot (α - δ)

is equal to