Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 77

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IMPORTANT

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All the values of $m$ for which both the roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ are greater than $- 2$ but less than $4$ lies in the interval

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Important Questions on Theory of Equations

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 78

If the roots of the quadratic equation

(4 p - p^{2} - 5) x^{2} - (2 p - 1) x + 3 p = 0

lie on either side of unity, then the number of integral values of

p

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 79

The interval of

a

for which the equation

\tan^{2} x - (a - 4) \tan x + 4 - 2 a = 0

has atleast one solution,

\forall x \in [0, \frac{π}{4}]

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 80

The range of

a

for which the equation

x^{2} + a x - 4 = 0

has its smaller root in the interval

(- 1, 2)

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 81

The set of all possible real values of

a

such that the inequality

(x - (a - 1)) (x - (a^{2} + 2)) < 0

holds for all

x \in (- 1, 3)

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 82

If the equation

\cot^{4} x - 2 {cosec}^{2} x + a^{2} = 0

has at least one solution, then the sum of all possible integral values of

a

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 83

If

a, b, c

are distinct positive numbers, then the nature of roots of the equation

\frac{1}{x - a} + \frac{1}{x - b} + \frac{1}{x - c} = \frac{1}{x}

is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 85

In the quadratic equation

4 x^{2} - 2 (a + c - 1) x + a c - b = 0; (a > b > c)

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Inequalities Involving Means>Exercises>Q 11

For

x^{2} - (a + 3) |x| + 4 = 0

to have real solutions, the range of

a

is