Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 123

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If two of the roots of equation $x^{4} - 2 x^{3} + a x^{2} + 8 x + b = 0$ are equal in magnitude but opposite in sign, then value of $4 a + b$ is equal to

50% studentsanswered this correctly

Important Questions on Quadratic Equations

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 124

If one root of equation

x^{2} - \sqrt{3} x + λ = 0, λ \in R

is

\sqrt{3} + 2

, then other root is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 125

If roots of equation

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

b, c \in R,

are real and distinct then the roots of equation

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

are

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 126

Let one root of the equation

x^{2} + l x + m = 0

is square of other root. If

m \in R

then

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 127

If

a, b

and

c

are integers and

b^{2} = 4 (a c + 5 d^{2}), d \in N

, then roots of the quadratic equation

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

are

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 128

Let

a, b

and

c

be real numbers such that

4 a + 2 b + c = 0

and

a b > 0

. Then the equation

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

has

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 129

Consider the equation

x^{2} + 2 x - n = 0,

where

n \in N

and

n \in [5, 100]

. Total number of different values of

n

so that the given equation has integral roots, is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 130

If

α

and

β (α < β)

are the roots of the equation

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

where

c < 0 < b,

then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 131

Which of the following graph represents the expression $f (x) = a x^{2} + b x + c (a \neq 0)$ , when $a > 0, b < 0$ and $c < 0$ ?