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Quantitative Aptitude

Solving Inequalities

Let f x = ax ...

Question

Let $f (x) = a x^{2} + b x + c$ , where a, b and c are certain constants and a is not 0. It is known that $f (5) = - 3 f (2)$ and that 3 is a root of f(x) = 0.
What is the other root of f(x) = 0?

A

-7

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B

-4

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C

2

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D

6

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E

Cannot be determined

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Solution

The correct option is B -4
Option (B) is the correct answer. Check the video for the approach.

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Similar questions

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

, where a, b and c are certain constants and a

\neq 0

. It is known that

f (5) = - 3 f (2)

and that 3 is a root of

f (x) = 0

.
What is the value of a + b + c?

Q. Statement 1 : If

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

a > 0, c < 0

b \in R

, then roots of

f (x) = 0

must be real and distinct .
Statement 2 : If

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

a > 0, b \in R, b \neq 0

and the roots of

f (x) = 0

are real and distinct, then

c

is necessarily negative real number .

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

g (x) = A x^{2} + b x + λ,

a \neq 0, A \neq 0, a, b, c, A, λ \in R

f (x) = 0

g (x) = 0

are imaginary, then which of the following may be correct?

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

g (x) = A x^{2} + b x + λ,

a \neq 0, A \neq 0, a, b, c, A, λ \in R

f (x) = 0

g (x) = 0

are imaginary, then which of the following may be correct?

Q. Statement-I : If

f (x)

is a quadratic expression such that

f (0) + f (1) = 0

- 2

f (x) = 0

, then the other root is

\frac{3}{5}

.
Statement-II : If

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

, then sum of roots

= - \frac{b}{a}

and product of roots

= \frac{c}{a} .

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