Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 11

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The integral values of $m$ for which the roots of equation $m x^{2} + (2 m - 1) x + (m - 2) = 0$ are rational are given by the expression [where $n$ is integer].

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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 12

x^{2} - x y + y^{2} - 4 x - 4 y + 16 = 0

represents

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 13

If the roots of the equation

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

are real and distinct and they differ by at most

2 m,

then

b

lies in the interval

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 14

If

x

is real, then

\frac{x}{(x^{2} - 5 x + 9)}

lies between

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 15

If

x^{2} + a x - 3 x - (a + 2) = 0

has real and distinct roots, then the minimum value of

\frac{(a^{2} + 1)}{(a^{2} + 2)}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 16

If

a, b, c, d \in R,

then the equation

(x^{2} + a x - 3 b) (x^{2} - c x + b) (x^{2} - d x + 2 b) = 0

has

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 17

If the roots of equation

(a - 1) {(x^{2} + x + 1)}^{2} = (a + 1) (x^{4} + x^{2} + 1)

are real and distinct, then the value of

a \in

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 18

If

b_{1} b_{2} = 2 (c_{1} + c_{2})

, then at least one of the equations

x^{2} + b_{1} x + c_{1} = 0

and

x^{2} + b_{2} x + c_{2} = 0

has

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 19

Suppose

A, B

and

C

are defined as

A = a^{2} b + a b^{2} - a^{2} c - a c^{2}, B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

and

C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

, where

a > b > c > 0

and the equation

A x^{2} + B x + C = 0

has equal roots, then

a, b

and

c

are in