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

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Let one root of the equation $x^{2} + l x + m = 0$ is square of other root. If $m \in R$ then

33.33% 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 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 $c < 0$ ?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 132

The expression

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

has always the same sign as of

a

if

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 133

The entire graph of the expression

y = x^{2} + k x - x + 9

is strictly above the

x

-axis if and only if

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 134

If

a, b \in R, a \neq 0

and the quadratic equation

a x^{2} - b x + 1 = 0

has imaginary roots then

a + b + 1

is