Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 26

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If $a {(p + q)}^{2} + 2 b p q + c = 0$ and $a {(p + r)}^{2} + 2 b p r + c = 0; (a \neq 0)$ , then

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Important Questions on Theory of Equations

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 27

If

α, β

are the nonzero roots of

a x^{2} + b x + c = 0

and

α^{2}, β^{2}

are the roots of

a^{2} x^{2} + b^{2} x + c^{2} = 0

, then

a, b, c

are in

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 28

If the roots of the equation

a x^{2} + b x + c = 0

are of the form

\frac{(k + 1)}{k} and \frac{(k + 2)}{(k + 1)} then {(a + b + c)}^{2}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 29

If

α, β

are the nonzero roots of

a x^{2} + b x + c = 0

and

α + h, β + h

are the roots of

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

, then

h

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 30

If one root of

x^{2} - x - k = 0

is square of the other, then the value of

k

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 31

If

α and β

be the roots of the equation

x^{2} + p x - \frac{1}{(2 p^{2})} = 0

. Where

p \in R

. Then the minimum value of

α^{4} + β^{4}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 32

If

α, β

are the roots of

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

and

γ, δ

are the roots of

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

, then

\frac{(α - γ) (α - δ)}{(β - γ) (β - δ)} =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 33

The value of

m

for which one of the roots of

x^{2} - 3 x + 2 m = 0

is double of one of the roots of

x^{2} - x + m = 0

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 34

If the equation

x^{2} - 3 p x + 2 q = 0

and

x^{2} - 3 a x + 2 b = 0

have a common root and the other root of the second equation is the reciprocal of the other root of the first, then

{(2 q - 2 b)}^{2}

is equal to