How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 61

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CAT

IMPORTANT

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If the equation $a x^{2} + b x + a = 0 (a > 0)$ has real and positive roots then which of the following is always 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 62

If

p, q, r

are real and

(x - p) (x - q) + (x - q) (x - r) + (x - r) (x - p) = 0

if

p \neq q \neq r

then which of the following options is true?

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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 63

If

f (x) = p x^{2} + q x + r & g (x) = r x^{2} + q x + p .

If one root of

f (x) = 0

is

2

and one root of

g (x) = 0

is

\frac{1}{4}

, then find the sum of the roots of

f (x)

and

g (x)

.

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 64

The number of distinct points at which the curve

y^{3} — 4 y^{2} + x^{2} — 5 x + 3 y = 0

intersects either the y-axis or the x-axis is _____.

MEDIUM

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 65

If the sum of the roots of the quadratic equation

{px}^{2} - 2 + qx + r = 0

is equal to the sum of the square of their reciprocals, mark the correct statements.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 1

f (x) = a x^{2} + b x + c & a < 0

The equation

f (x) = 0

has two distinct roots which is from the set

{- 2, - 1, 0, 1, 2}

. How many different pairs of roots of

f (x)

are possible such that

f (0)

is greater than or equals to

0

?

MEDIUM

CAT

IMPORTANT

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

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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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)

.