Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 71

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If the equation $a x^{2} + b x + c = x$ has no real roots, then the equation $a {(a x^{2} + b x + c)}^{2} + b (a x^{2} + b x + c) + c = x$ will have

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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 72

If

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

has imaginary roots and

a - b + c > 0,

then the set of points

(x, y)

satisfying the equation

|a (x^{2} + \frac{y}{a}) + (b + 1) x + c| = |a x^{2} + b x + c| + |x + y|

consists of the region in the

x y

-plane which is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 73

Given

x, y \in R, x^{2} + y^{2} > 0 .

Then the range of

\frac{x^{2} + y^{2}}{x^{2} + x y + 4 y^{2}}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 74

If

x_{1}

and

x_{2}

are the roots of

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

and

x_{1} x_{2} < 0

, then the roots of

x_{1} {(x - x_{2})}^{2} + x_{2} {(x - x_{1})}^{2} = 0

are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 75

If

a, b, c, d

are four consecutive terms of an increasing

A . P .

, then the roots of the equation

(x - a) (x - c) + 2 (x - b) (x - d) = 0

are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 76

If roots of

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

are such that at least one of them is greater than

2,

then

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

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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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