Let f(x) be a quadratic polynomial such that f(--1) + f(2) = 0.

Question

Let f(x) be a quadratic polynomial such that

f(--1) + f(2) = 0. If one of the roots of f(x) = 0

is 3, then its other root lies in :

Accepted Answer

Let the other root is $$\alpha $$.

$$ \therefore $$ f(x)

=

a(x

--

3)

(x

--

$$\alpha $$)

f(2) = a($$\alpha $$-- 2)

f(--1) = 4a(1 + $$\alpha $$)

Given f(--1) + f(2) = 0

$$ \Rightarrow $$a($$\alpha $$ -- 2 + 4 + 4$$\alpha $$) = 0

$$ \Rightarrow $$ 5$$\alpha $$ = -2      As a $$ \ne $$ 0

$$ \Rightarrow $$ $$\alpha $$ = $$-\frac{2}{5} $$ = - 0.4

$$ \therefore $$ $$\alpha $$ $$ \in $$ (--1, 0)

Solutions · 1