How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 2

MEDIUM

CAT

IMPORTANT

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$p x^{2} + q x + r = 0$ has one root greater than $3$ and the other root less than $1 .$ Which of the following is necessarily true?

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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 3

If

f (x, y) = 4^{x^{y}} + x^{4^{y}}

, then what is the total number of solutions for the equation

f (x, y) = 5

.

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 6

The values of a quadratic function

f (x)

is positive for all values of

x

, except for

x = 4

. If

f (0) = 10

. Find the value of

f (— 4)

.

MEDIUM

CAT

IMPORTANT

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

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

.

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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

.