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Mathematical Statements

If a < 0, t...

Question

If $a < 0$ , then function $f (x) = a x^{2} + b x + c$ has

A

minimum value.

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B

constant value.

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C

maximum value.

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D

positive value.

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Solution

The correct option is D maximum value.
When $a < 0$ , $f (x)$ has maximum value because as we increase the value of $x$ the value of $f (x)$ keeps on decreasing as shown

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a < 0

, then the function

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

k \in R

lies between the roots of

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

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

f (k)

&

ϵ

R such that a + b + c = 0 and a + b - c = 0, then the polynomial function

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

(a > 0)

attains its least value at 'x' equal to

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

has no real zeroes and

a + b + c < 0

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

has no real zeros and

a + b + c < 0

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