Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 40

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

If the roots of $x^{2} - a x + b = 0$ are two consecutive odd integers, then $a^{2} - 4 b$ is equal to

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Important Questions on Inequalities and Quadratic Equation

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 41

If

α

and

β

are the roots of

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

then

α^{2} + β^{2}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 42

If

α

and

β

are the roots of the equation

x^{2} + 3 x - 4 = 0,

then

\frac{1}{α} + \frac{1}{β}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 43

If the roots of the equation

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

are

α

and

β,

then

b^{2} - c

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 44

If

a, b

and

c

are positive numbers in a

G P

, then the roots of the quadratic equation

(\log_{e} a) x^{2} - (2 \log_{e} b) x + (\log_{e} c) = 0

are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 46

Let

f (x) = 2 x^{2} + 5 x + 1 .

If we write

f (x)

as

\begin{array}{r} f (x) = \end{array} a (x + 1) (x - 2) + b (x - 2) (x - 1) + c (x - 1) (x + 1)

for real numbers

a, b

and

c,

then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 47

If

α

and

β

are the roots of the equation

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

and

S_{n} = α^{n} + β^{n}

, then

a S_{n + 1} + b S_{n} + c S_{n - 1}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 48

If the roots of

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

are

\sin α

and

\cos α

for some

α,

then which one of the following is correct?

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 5 - Inequalities and Quadratic Equation>Entrances Gallery>Q 49

The value of

x

such that

3^{2 x} - 2 (3^{x + 2}) + 81 = 0

is