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

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Consider equation $(x - \sin α) (x - \cos α) - 2 = 0$ . Which of the following is $/$ are true $?$

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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 34

If the roots of the equation

x^{3} + p x^{2} + q x - 1 = 0

form an increasing G.P. where

p

and

q

are real, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 35

If roots of

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

are

α

and

β

and

4 a + 2 b + c > 0

,

4 a - 2 b + c > 0

, and

c < 0

, then possible value/values of

[α] + [β]

is/are (where

[\cdot]

represents greatest integer function)

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 36

The equation

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

has

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 37

If the quadratic equations,

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

and

b x^{2} + c x + 1 = 0

have a common root then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 38

If the inequality

\cot^{2} x + (k + 1) \cot x - (k - 3) < 0

is true for at least one

x \in (0, \frac{π}{2})

, then

k \in

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

If

x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}

then the value of

x^{3} - 6 x^{2} + 6 x

is .

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

If

\sqrt{\sqrt{\sqrt{x}}} = \sqrt[4]{\sqrt[4]{\sqrt[4]{3 x^{4} + 4}}},

then the value of

x^{4}

is .

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

Sum of the values of

x

satisfying the equation

\sqrt{2 x + \sqrt{2 x + 4}} = 4

is