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

EASY

CAT

IMPORTANT

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For what value of c the quadratic equation $x^{2} - (c + 6) x + 2 (2 c - 1) = 0$ has sum of the roots as half of their product?

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Important Questions on Quadratic and Other Equations

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 12

Two numbers

a

and

b

are such that the quadratic equation

a x^{2} + 3 x + 2 b = 0

has

- 6

as the sum and the product of the roots. Find

a + b

.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 13

If

α

and

β

are the roots of the quadratic equation

5 y^{2} - 7 y + 1 = 0

then find the value of

\frac{1}{α} + \frac{1}{β}

.

EASY

CAT

IMPORTANT

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

Find the value of the expression

(\sqrt{x + (\sqrt{x + (\sqrt{x . . . +})})})

.

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 15

If

a = \sqrt{(7 + 4 \sqrt{3}})

, what will be the value of

(a + \frac{1}{a})

?

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 16

If the roots of the equation

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

are equal then

a, b, c

are in:

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 17

If

α

and

β

are the roots of the equation

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

then the equation whose roots are

α + \frac{1}{β}

and

β + \frac{1}{α}

is:

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 18

If

x^{2} + a x + b

leaves the same remainder

5

when divided by

x - 1

or

x + 1

then the values of

a

and

b

are respectively:

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 22 - Quadratic and Other Equations>Level of Difficulty>Q 19

Find all the values of b for which the equation

x^{2} - b x + 1 = 0

does not possess real roots.