Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 9

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Let $- \frac{π}{6} < θ < - \frac{π}{12} .$ Suppose $α_{1}$ and $β_{1}$ are the roots of the equation $x^{2} - 2 x \sec θ + 1 = 0$ and $α_{2}$ and $β_{2}$ are the roots of the equation $x^{2} + 2 x \tan θ - 1 = 0 .$ If $α_{1} > β_{1}$ and $α_{2} > β_{2},$ then $α_{1} + β_{2}$ equals?

16.67% studentsanswered this correctly

Important Questions on Quadratic Equations

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 10

A value of $b$ for which the equations $x^{2} + b x - 1 = 0$ and $x^{2} + x + b = 0$ have one root in common is?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 12

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots.

(4, 3) .

Rahul made a mistake in writing down the coefficient of

x

to get roots

(3, 2) .

The correct roots of the equation are?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 13

Let for

a \neq a_{1} \neq 0

,

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

,

g (x) = a_{1} x^{2} + b_{1} x + c_{1}

and

p (x) = f (x) - g (x) .

If

p (x) = 0

only for

x = - 1

and

p (- 2) = 2,

then the value of

p (2)

is?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 14

The equation

e^{\sin x} - e^{- \sin x} - 4 = 0

has ?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 15

If the equations

x^{2} + 2 x + 3 = 0

and

a x^{2} + b x + c = 0, a, b, c \in R

, have a common root, then

a : b : c

is?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 16

If

a \in R

and the equation

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

(where

[x]

denotes the greatest integer

\leq x

) has no integral solution, then all possible values of

a

lie in the interval:

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 17

Let

α

and

β

be the roots of equation

{px}^{2} + qx + r = 0, p \neq 0 .

If

p, q, r

are in

A . P .

and

\frac{1}{α} + \frac{1}{β} = 4,

then the value of

|α - β|

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 18

Let

α

and

β

be the roots of equation

x^{2} - 6 x - 2 = 0 .

If

a_{n} = α^{n} - β^{n},

for

n \geq 1,

then the value of

\frac{a_{10} - 2 a_{8}}{2 a_{9}}

is equal to