If f(x) is a quadratic expression such that f(1)+f(2)=0 and -1 is a root of f(x)=0, then t…

Question

If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$ and $-1$ is a root of $f(x)=0$, then the other root of $f(x)=0$ is

Accepted Answer

Let $$\alpha $$ and $$\beta $$ = - 1 are the roots of the polynomial, then we get

f(x) = x2 + (1 - $$\alpha $$)x - $$\alpha $$

$$ \therefore $$ f(1) = 2 - 2$$\alpha $$

and f(2) = 6 - 3$$\alpha $$

Also given,

f (1) + f (2) = 0

$$ \therefore $$ 2 - 2$$\alpha $$ + 6 - 3$$\alpha $$ = 0

$$ \Rightarrow $$ $$\alpha $$ = $${8 \over 5}$$

Solutions · 1