Question

let f(x) be a quadratic polynomial with f(2) = 10 and f(-2) =2 then the coefficient of x in f(x)​

Answer 1

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Let the quadratic equation be f(x)=x2+ax+b

Given f(2)=10 and f(−2)=−2

⇒4+2a+b=10 and 4−2a+b=−2

⇒2a+b=6 and 2a−b=6

on solving both equations , we get a=3 and b=0

Therefore, the coefficient of x in f(x) is 3.

Answer 2

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$\bold{Let \: the \: quadratic \: equation \: be \: f(x)=x }$

$\bold{2 + ax + b}$

$\bold{Given \: f(2)=10 \: and \: f(−2)=−2}$$\bold{⇒4+2a+b=10 \: and \: 4−2a+b=−2}\\\bold{⇒2a+b=6 \: and \: 2a−b=6}$

$\bold{ \: solving \: equations \: , we \: get \: a=3 \: and \: b=0}$

$\bold{Therefore, the \: coefficient \: of \: x \: in \: f(x) \: is \: 3.}$