Let f(x) be a quadratic polynomial such that f(-2)+f(3)=0.

Question

Let $f(x)$ be a quadratic polynomial such that $f(-2)+f(3)=0$. If one of the roots of $f(x)=0$ is $-1$, then the sum of the roots of $f(x)=0$ is equal to:

Accepted Answer

$$\because$$ x = -1 be the roots of f(x) = 0

$$\therefore$$ Let $f(x) = A(x + 1)(x - 1)$ ...... (i)

Now, $f( - 2) + f(3) = 0$

$$ \Rightarrow A[ - 1( - 2 - b) + 4(3 - b)] = 0$$

$$b = {{14} \over 3}$$

$$\therefore$$ Second root of f(x) = 0 will be $${{14} \over 3}$$

$$\therefore$$ Sum of roots $$ = {{14} \over 3} - 1 = {{11} \over 3}$$

Solutions · 1