Question

The zeros of the polynomial $x^2-\sqrt{2}x-12$ are _____

• A. $\sqrt{2},-\sqrt{2}$
• B. $3\sqrt{2},-2\sqrt{2}$
• C. $3-\sqrt{2},2\sqrt{2}$
• D. $3\sqrt{2},2\sqrt{2}$

Answer 1

The correct option is B $3\sqrt{2},-2\sqrt{2}$

Given, $x^2-\sqrt{2}x-12$
$\text{Let's factorise using formula}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}a=1;b=-\sqrt{2};c=-12x=\frac{-(-\sqrt{2})\pm \sqrt{(-\sqrt{2}{)}^2-4\times 1\times (-12)}}{2\times 1}=\frac{\sqrt{2}\pm \sqrt{2+48}}{2}=\frac{\sqrt{2}\pm \sqrt{50}}{2}=\frac{\sqrt{2}\pm \sqrt{2\times 5\times 5}}{2}=\frac{\sqrt{2}\pm 5\sqrt{2}}{2}x=\frac{\sqrt{2}+5\sqrt{2}}{2};\frac{\sqrt{2}-5\sqrt{2}}{2}=\frac{6\sqrt{2}}{2};\frac{-4\sqrt{2}}{2}x=3\sqrt{2};-2\sqrt{2}\text{Zeroes are}3\sqrt{2}\&-2\sqrt{2}$