The zeros of the polynomial
Question:

The zeros of the polynomial $4 x^{2}+5 \sqrt{2} x-3$ are

(a) $-3 \sqrt{2}, \sqrt{2}$

(b) $-3 \sqrt{2}, \frac{\sqrt{2}}{2}$

(c) $\frac{-3 \sqrt{2}}{2}, \frac{\sqrt{2}}{4}$

(d) none of these

Solution:

(c) $-\frac{3}{\sqrt{2}}, \frac{\sqrt{2}}{4}$

Let $f(x)=4 x^{2}+5 \sqrt{2} x-3=0$

$=>4 x^{2}+6 \sqrt{2} x-\sqrt{2} x-3=0$

$=>2 \sqrt{2} x(\sqrt{2} x+3)-1(\sqrt{2} x+3)=0$

$=>(\sqrt{2} x+3)(2 \sqrt{2} x-1)=0$

$=>x=-\frac{3}{\sqrt{2}}$ or $x=\frac{1}{2 \sqrt{2}}$

$=>x=-\frac{3}{\sqrt{2}}$ or $x=\frac{1}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{4}$

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