Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 87

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The equation $2^{2 x} + (a - 1) 2^{x + 1} + a = 0$ has roots of opposite signs, then exhaustive set of values of $a$ is

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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 88

The set of values of

a

for which

a x^{2} + (a - 2) x - 2

is negative for exactly two integral

x

, is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 89

If

a_{0}, a_{1}, a_{2}, a_{3}

are all positive, then

4 a_{0} x^{3} + 3 a_{1} x^{2} + 2 a_{2} x + a_{3} = 0

has at least one root in

(- 1, 0)

if

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 1

If

c \neq 0

and the equation

\frac{p}{2 x} = \frac{a}{x + c} + \frac{b}{x - c}

has two equal roots, then

p

can be

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

If

α, β

are the roots of the quadratic equation

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

, then which of the following expression will be the symmetric function of roots

?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 3

If one root of the quadratic equation

p x^{2} + q x + r = 0; (p \neq 0)

is

\frac{\sqrt{a}}{\sqrt{a} + \sqrt{a - b}}

, where

p, q, r \in Q

, and

a, b

are positive integers which are not perfect square of any integer, then the other root is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 4

If

a, b, c

are in

GP

, then the roots of the equation

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

are in the ratio

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 5

Roots of the equation

{(a + \sqrt{b})}^{x^{2} - 15} + {(a - \sqrt{b})}^{x^{2} - 15} = 2 a

, where

a^{2} - b = 1

, are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 6

If the equations

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

and

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

have a common root, then it must be equal to