Question:
The zeros of the polynomial $7 x^{2}-\frac{11}{3} x-\frac{2}{3}$ are
(a) $\frac{2}{3}, \frac{-1}{7}$
(b) $\frac{2}{7}, \frac{-1}{3}$
(c) $\frac{-2}{3}, \frac{1}{7}$
(d) none of these
Solution:
(a) $\frac{2}{3}, \frac{-1}{7}$
Let $f(x)=7 x^{2}-\frac{11}{3} x-\frac{2}{3}=0$
$\Rightarrow 21 x^{2}-11 x-2=0$
$\Rightarrow 21 x^{2}-14 x+3 x-2=0$
$\Rightarrow 7 x(3 x-2)+1(3 x-2)=0$
$\Rightarrow(3 x-2)(7 x+1)=0$
$\Rightarrow x=\frac{2}{3}$ or $x=\frac{-1}{7}$
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