Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 13

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Find the least prime integral value of $2 a$ such that the roots $α, β$ of the equation $2 x^{2} + 6 x + a = 0$ satisfy the inequality $\frac{α}{β} + \frac{β}{α} < 2$ .

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Important Questions on Quadratic Equations

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 14

If $α, β$ are roots of the equation $λ (x^{2} - x) + x + 5 = 0 .$ If $λ_{1}$ and $λ_{2}$ are the two values of $λ$ for which the roots $α, β$ are connected by the relation $\frac{α}{β} + \frac{β}{α} = 4,$ then the value of $(\frac{\frac{λ_{1}}{λ_{2}} + \frac{λ_{2}}{λ_{1}}}{14})$ is

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Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 15

Suppose that the two roots of the equation

\frac{1}{x^{2} - 10 x - 29} + \frac{1}{x^{2} - 10 x - 45} - \frac{2}{x^{2} - 10 x - 69} = 0

are

α

and

β .

Find the value of

(- α β) .

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Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 16

For how many real values of

a

will

x^{2} + 2 a x + 2008 = 0

has two integer roots?

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Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 17

Natural numbers

k, l, p

and

q

are such that if

a

and

b

are roots of

x^{2} - k x + I = 0

then

a + \frac{1}{b}

and

b + \frac{1}{a}

are the roots of

x^{2} - p x + q = 0 .

What is the sum of all possible values of

q

?

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Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 18

If

λ_{1}

and

λ_{2}

are the two values of

λ

, such that the roots

α

and

β

of the quadratic equation,

λ (x^{2} - x) + x + 5 = 0

satisfy

\frac{α}{β} + \frac{β}{α} + \frac{4}{5} = 0,

then

\frac{λ_{1}}{λ_{2}^{2}} + \frac{λ_{2}}{λ_{1}^{2}}

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 19

If

α

and

β

be the roots of the equation

x^{2} + 3 x + 1 = 0

, then the value of

{(\frac{α}{1 + β})}^{2} + {(\frac{β}{α + 1})}^{2}

is equal to

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Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 20

Let

f (x) = a x^{2} + b x + c, g (x) = a x^{2} + q x + r

, where

a, b, c, q, r \in R

and

a < 0

. If

α, β

are the roots of

f (x) = 0

and

α + δ, β + δ

are the roots of

g (x) = 0

, then

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 24 - Quadratic Equations>Level 2>Q 21

A quadratic equation whose product of roots

x_{1}

and

x_{2}

is equal to

4

and satisfying the relation

\frac{x_{1}}{(x_{1} - 1)} + \frac{x_{2}}{(x_{2} - 1)} = 2

is