Let f(x) be a quadratic polynomial in x such that f(x)\geq 0 for all real numbers x. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

CAT 2022 Slot 2 Paper

Question : 50 of 66

Marks: +1, -0

Let $f(x)$ be a quadratic polynomial in $x$ such that $f(x)≥ 0$ for all real numbers $x$ . If $f(2) = 0$ and $f( 4) = 6$ , then $f(-2)$ is equal to

Validate

Solution:

f(x) ≥ 0

for all real numbers

x

, so

\D< =0

Since

f(2)=0

therefore

x=2

is a root of

f(x)

Since the discriminant of

f(x)

is less than equal to 0 and 2 is a root so we can conclude that

\D=0

Therefore

{f}( {x})=a(x-2)^2

f(4)=6

or,

6=a(x-2)^2

a=3 / 2

f(-2)=-{3}/{2}(-4)^2=24

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