Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 17

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Earn 100

Suppose that $f (x)$ is a quadratic expression positive for all real $x .$ If $g (x) = f (x) + f^{'} (x) + f^{''} (x),$ then for any real $x$ (where $f^{'} (x)$ and $f^{''} (x)$ represent ( $1^{st}$ and $2^{nd}$ derivative, respectively)

50% studentsanswered this correctly

Important Questions on Quadratic Equations

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 18

Let

f (x) = a x^{2} - b x + c^{2}, b \neq 0

and

f (x) \neq 0

for all

x \in R

. Then,

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 19

If roots of

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

are such that at least one of them is greater than

2

, then

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 20

Total number of values of

a

so that

x^{2} - x - a = 0

has integral roots, where

a \in N

and

6 \leq a \leq 100

is equal to

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 21

The number of values of

k

for which

[x^{2} - (k - 2) x + k^{2}] \cdot [x^{2} + k x + (2 k - 1)]

is a perfect square is

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 22

If

α, β

are the roots of

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

and

x^{2 n} + p^{n} x^{n} + q^{n} = 0

and if

(\frac{α}{β}), (\frac{β}{α})

are the roots of

x^{n} + 1 + {(x + 1)}^{n} = 0,

then

n (\in N)

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 23

If

x y = 2 (x + y), x \leq y

and

x, y \in N

, then the number of solutions of the equation are

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 24

If

α, β, γ

are such that

α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8,

then

α^{4} + β^{4} + γ^{4}

is

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 5 - Quadratic Equations>Exercise>Q 25

The number of real solutions of the equation

{(\frac{9}{10})}^{x} = - 3 + x - x^{2}

is