Question

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

• A. $-3\sqrt{2},\frac{\sqrt{2}}{2}$
• B. $-3\sqrt{2},\sqrt{2}$
• C. $\frac{-3\sqrt{2}}{2},\frac{\sqrt{2}}{4}$
• D. $-6\sqrt{2},2\sqrt{2}$

Answer 1

The correct option is C $\frac{-3\sqrt{2}}{2},\frac{\sqrt{2}}{4}$

$\text{Given},4x^2+5\sqrt{2}x-3\text{Lets factorize using Formula}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}a=4;b=5\sqrt{2};c=-3x=\frac{-5\sqrt{2}\pm \sqrt{(5\sqrt{2}{)}^2-4\times 4\times (-3)}}{2\times 4}=\frac{-5\sqrt{2}\pm \sqrt{25\times 2+48}}{8}=\frac{-5\sqrt{2}\pm \sqrt{98}}{8}=\frac{-5\sqrt{2}\pm \sqrt{49\times 2}}{8}=\frac{-5\sqrt{2}\pm 7\sqrt{2}}{8}x=\frac{-5\sqrt{2}+7\sqrt{2}}{8};\frac{-5\sqrt{2}-7\sqrt{2}}{8}=\frac{2\sqrt{2}}{8};\frac{-12\sqrt{2}}{8}x=\frac{\sqrt{2}}{4};\frac{-3\sqrt{2}}{2}\text{Zeroes are}\frac{\sqrt{2}}{4}\&\frac{-3\sqrt{2}}{2}$