How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 7

MEDIUM

CAT

IMPORTANT

Earn 100

Find all values of $' a'$ , such that $4$ lies somewhere between the roots of the equation $3 x^{2} + 4 ax + (a + 3) = 0$ for all values of $x$ .

50% studentsanswered this correctly

Important Questions on Quadratic and Other Equations

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 8

f (x) = x^{3} — (5 + k) x^{2} + (6 + 5 k) x — 6 k

, where

' k'

is an odd prime number and

k > 3

. What is the range of values of

x

for which

f (x) < 0

.

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 9

If

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

, where

a, b, c

are constants and

a < 0

and

' p'

is a natural number. It is given that the roots of the equation

{ax}^{2} + bx + c = 0

are

3, 4

. Then, the value of

x

at which

f (x, 5)

attains its maximum value is:

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 10

f (x) = {[x]}^{2} — 11 [x] + 30

, where

[x]

represents the largest integer less than or equal to

x

, then what is the sum of all integer solutions of the equation

f (x) = 0

.

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 11

If all the three roots of the equation

x^{3} — 12 x^{2} + px — 42 = 0

are unequal and prime. Then

p = ?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 14

If

f (x) = (b - 1) x^{2} + (c + d) x + e

and

a : b = 1 : 2, b : c = 2 : 3, c : d = 3 : 4, d : e = 4 : 5

. Then find the square of the difference of the roots of the equation

f (x) = 0

.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 23

The value of

p

for which the sum of the square of the roots of the equation

x^{2} - (p - 3) x + (p - 4) = 0

is minimum is:

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 24

If

f (x) = x^{2} . g (x) = x^{3} - 2^{x}

, where

x

is a positive integer then for how many values of

x

is

f (x) = g (x)

.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 27

The curve, shown below can possibly represent which of the following equation? (Assume the curve does not exist at $x = 0$ ).

Question Image