Question

the zeros of the polynomial 4xsquare + 5root2x - 3 are ​

Answer 1

$\huge\mathbb{SOLUTION :-}$

• We have to find the zero's of polynomial

$\bf\underline{\underline{\red{According\:To\: Question:-}}}$

$\sf\implies 4x{}^{2}+5\sqrt{2}x-3=0\\ \\ \sf \:\: multiply\: 3\: with \:4=12\:\ and\: \:\\ \\ \sf take\: factor\: of\:12 \\ \\ \sf it\: is\: write\:as \:6\sqrt{2}-\sqrt{2}\\ \\ \sf\implies 4x{}^{2}-(6\sqrt{2}-\sqrt{2})x-3=0\\ \\ \sf\implies 4x{}^{2}-6\sqrt{2}x+\sqrt{2}x-3=0\\ \\ \sf\implies 2\sqrt{2}x(\sqrt{2x}-3)+1(\sqrt{2x}-3)=0\\ \\ \sf\implies (\sqrt{2}x-3)(2\sqrt{2x}+1)=0$

• Now the zero's of polynomial

$\sf\implies \:\: \sqrt{2}x-3=0\\ \\ \sf\implies \sqrt{2}x=3\\ \\ \sf\implies x=\frac{3}{\sqrt{2}}$

• Now 2nd zero

$\sf\implies 2\sqrt{2}x+1=0\\ \\ \sf\implies 2\sqrt{2}x=(-1)\\ \\ \sf\implies x=\frac{(-1)}{2\sqrt{2}}$

$\underline{\boxed{\sf{\purple{Zero's= \frac{3}{\sqrt{2}}\:\:and\: \frac{(-1)}{2\sqrt{2}}}}}}$