Question

The zeros of the polynomial 2 − √2 − 12 are

a) √2, −√2 b) 3√2, 2√2 c) −3√2, 2√2 d) none of these​

Answer 1

$\mathtt{p(x) = 2x²-√2x-12}$

$\mathtt{\;\;\;\;\;\;\; = 2x²-4√2x+3√2x-12}$

$\mathtt{\;\;\;\;\;\;\; = 2x(x-2√2)+3√2(x-2√2)}$

$\mathtt{\;\;\;\;\;\;\; = (x-2√2) (2x+3√2) }$

$\texttt{If} \; \mathtt{p(x) = 0}$

$\implies \mathtt{(x-2√2) (2x+3√2) = 0}$

$\implies \mathtt{(x-2√2)=0} \;\;\;\;\; \texttt{or} \;\;\;\;\; \mathtt{(2x+3√2) = 0}$

$\implies \mathtt{x=2√2} \;\;\;\;\; \texttt{or} \;\;\;\;\; \mathtt{x = \Large\frac{-3√2}{2}}$