Question

if f(x) be a quadratic polynomial such that F(2) = -3 and F(-2) = 21 find the coefficient of X in f(X)

Answer 1

Let
$f(x)=ax^2+bx+c\\f(2)=4a+2b+c=-3\qquad\boxed{1}\\f(-2)=4a-2b+c=21\qquad\boxed{2}\\\text{Subtract }\boxed{1}-\boxed{2},\\4b=-24\\b=-6\\f(X)=aX^2+bX+c\\\text{Coefficient of X}=b=-6$