Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 37

EASY

CAT

IMPORTANT

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The condition that both the roots of quadratic equation ${ax}^{2} + bx + c = 0$ are positive is

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Important Questions on X+2 Maths

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 38

The condition that both the roots of the equation

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

are zero is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 39

There is a quadratic equation of the form

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

along with

3

conditions.

I. If only the value of $a$ is correct in the equation, the roots are $\frac{1}{3}$ and 1 .

II. If only the value of $b$ is correct, the roots are $6$ and $5$ .

III. If only the value of $c$ is correct, the roots are $- 3$ and $- 2$ .

What is the equation of a quadratic equation opposite in sign to the roots of the given quadratic equation?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 40

Quadratic equations

(2 p - 1) z^{2} + (2 p + 1) z + c = 0

and

(q + 1) y^{2} + (4 q + 1) y + 3 c = 0

have the same pair of roots. Given that

c \neq 0

, what is the value of

(p + q)

?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 1

Quadratic equation

x^{2} + bx + c =

has roots a and b, such that LCM of

(a, b) = 24

and HCF of

(a, b) = 2

. What is the total number of such quadratic equations if a and b are natural numbers?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 2

If

(p^{2} + q^{2}) x^{2} - \sqrt{2} (p + q) x + 1 = 0

, what must be the relation between

q

and

p

if the equation has equal and real roots?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 3

How many positive integers p, q, and r exist such that

\frac{p}{q} + \frac{q}{r} + \frac{r}{p} = 2

?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 4

If

x^{2} + y^{2} + z^{2} = 1

, then the value of

x y + y z + z x

lies in the interval of:

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 5

If

a \in R, b \in R,

then the factors of the expression

a (x^{2} - y^{2}) - b x y

are