Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 6

HARD

JEE Main

IMPORTANT

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If $a > 1$ , then the roots of the equation $(1 - a) x^{2} + 3 a x - 1 = 0$ are

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Important Questions on Theory of Equations

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 7

The values of

a

, for which the quadratic expression

a x^{2} + (a - 2) x - 2

is negative for exactly two integral values of

x

, belongs to

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 8

The values of

a

for which the roots of the equation

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

,

(a \neq - 1)

are real and greater than

1

are

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JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 9

The equation

a x^{4} - 2 x^{2} - (a - 1) = 0

will have real and unequal roots if

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 10

If

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

,

a \neq 0

,

a

,

b

,

c \in R

has distinct real roots in

(1, 2)

, then

a

and

5 a + 2 b + c

have

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 11

If

c < a < b < d

, then the roots of the equation

b x^{2} + (1 - b (c + d)) x + b c d - a = 0

are

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 12

If

2 a

,

b

,

2 c

are in

A.P.

, where

a

,

b

and

c

are

R^{+}

, then the expression

f (x) = (a x^{2} - b x + c)

has

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 13

If

a

,

b

and

c

are positive numbers, such that

a > b > c

, and the equation

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

has a root in the interval

(- 1

,

0)

, then

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 2 - Theory of Equations>DPP>Q 14

If the quadratic equation

x^{2} - 36 x + λ = 0

has roots

α

and

β

, such that

α

,

β \in N

and

\frac{λ}{5} \notin Z

and

λ

assumes the minimum possible value, then

\frac{\sqrt{α + 2} \sqrt{β + 2}}{| α - β |}

is equal to