Question

Write standard form of quadratic equation and find the roots of the equations $3x^2+5\sqrt{2}+2=0$ using general formula.

Answer 1

The polynomial of degree 2 is called quadratic polynomial and $a{x}^2+bx+c=0$ where$a\ne 0$ is standard form of quadratic equation.

Given:$P\left(x\right)=3x^2+5\sqrt{2}x+2$

Here $a=3$

$b=5\sqrt{2}$

$c=2$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-5\sqrt{2}\pm \sqrt{50-4\times 3\times 2}}{2\times 3}$

$x=\frac{-5\sqrt{2}\pm \sqrt{26}}{6}$

So, $x=\frac{-5\sqrt{2}+\sqrt{26}}{6}$ , $x=\frac{-5\sqrt{2}-\sqrt{26}}{6}$