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 the quadratic polynomial be
f(x) =ax²+bx+c
Now,
f(2) =a×(2)²+b×2+c →4a+2b+c=−3.........(i)
and f(−2) =a×(−2)²+b×(−2)+c →4a−2b+c=21.........(ii)
Subtracting (ii) from (i) gives 4b=−24 i.e. b=−24/4=−6......(iii)
Coefficient of 'x' is −6