Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 27

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Two roots of a biquadratic $x^{4} - 18 x^{3} + k x^{2} + 200 x - 1984 = 0$ have their product equal to $(- 32)$ , then the value of $k$ , is

50% studentsanswered this correctly

Important Questions on Quadratic Equations

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 28

α, β

are the roots of the equation

K (x^{2} - x) + x + 5 = 0

. If

K_{1}

&

K_{2}

are the two values of

K

for which the roots,

α, β

are connected by the relation

(α / β) + (β / α) = 4 / 5

. Find the value of

(K_{1} / K_{2}) + (K_{2} / K_{1})

.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 29

Let

P (x) = x^{2} + b x + c

, where

b

and

c

are integer. If

P (x)

is a factor of both

x^{4} + 6 x^{2} + 25

and

3 x^{4} + 4 x^{2} + 28 x + 5

, then the value of

P (1)

is

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 30

The true set of values of

p

for which the equation:

p \cdot 2^{\cos^{2} x} + p \cdot 2^{- \cos^{2} x} - 2 = 0

has real roots, is

[\frac{a}{b}, c]

, where

H . C . F

.

(a, b) = 1

and

a, b, c \in N

, then value of

a + b + c

is

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 31

If the three equations

x^{2} + a x + 12 = 0, x^{2} + b x + 15 = 0

and

x^{2} + (a + b) x + 36 = 0

have a common positive root, then value of

a + b

is

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-3>Q 32

A quadratic polynomial

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

is formed with one of its zeros being

\frac{4 + 3 \sqrt{3}}{2 + \sqrt{3}}

, where

a

and

b

are integers. Also,

g (x) = x^{4} + 2 x^{3} - 10 x^{2} + 4 x - 10

is a biquadratic polynomial such that

g (\frac{4 + 3 \sqrt{3}}{2 + \sqrt{3}}) = c \sqrt{3} + d

, where

c

and

d

are also integers. Then the value of

a + b + c + d

, is

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-4>Q 1

Find the domain & range of the following functions

$y = \frac{2 x}{1 + x^{2}}$

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-4>Q 2

Find the domain & range of the following functions

$y = \sqrt{2 - x} + \sqrt{1 + x}$

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>EXERCISE-4>Q 3

Find the domain & range of the following functions

$y = \sin (x^{2} - 3 x + 2)$