Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 39

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If $a, b, c$ are non-zero real numbers, then the minimum value of the expression $(\frac{(a^{4} + 3 a^{2} + 1) (b^{4} + 5 b^{2} + 1) (c^{4} + 7 c^{2} + 1)}{a^{2} b^{2} c^{2}})$ 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 40

If

a, b \in R

such that

a + b = 1

and

(1 - 2 a b) (a^{3} + b^{3}) = 12 .

The value of

(a^{2} + b^{2})

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 41

If the cubic equation

2 x^{3} - 9 x^{2} + 12 x + k = 0

has two equal roots then maximum value of

|k|

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 42

Let

a, b

and

c

be distinct non-zero real numbers such that

\frac{1 - a^{3}}{a} = \frac{1 - b^{3}}{b} = \frac{1 - c^{3}}{c} .

The value of

(a^{3} + b^{3} + c^{3})

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 43

If the fraction

\frac{x^{3} + (a - 10) x^{2} - x + a - 6}{x^{3} + (a - 6) x^{2} - x + a - 10}

reduces to a quotient of two linear functions, then

a

equals .

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

If the roots of the equation

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

are imaginary, then for all real values of

x

, the expression

3 b^{2} x^{2} + 6 b c x + 2 c^{2}

is

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

The equation $e^{\sin x} - e^{- \sin x} - 4 = 0$ has

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

If the equations

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

and

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

a, b, c \in R,

have a common root, then

a : b : c

is

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

Let

α

and

β

be the roots of equation

{px}^{2} + qx + r = 0, p \neq 0 .

If

p, q, r

are in

A . P .

and

\frac{1}{α} + \frac{1}{β} = 4,

then the value of

|α - β|

is