Question

ILLUSTRATION 2.1
Letf(x) be a quadratic polynomial satisfying f (2) + f(4) = 0.
If unity is one root of f(x)=0 then find the other root.​

Answer 1

From the given information,

f(x)=(x−1)(ax+b)

So, f(2)=2a+b

and " " f(4)=3(4a+b)=12a+3b

Given that f(2)+f(4)=0

⇒ 14a+4b=0

⇒ b=−7a2

∴ Equationis(x−1)(ax−7a2)=0

Therefore, other root is 7/2