Question

The given quadratic equations have real roots and roots are $\frac{\sqrt{5}}{3},-\sqrt{5}$ :
$3x^2+2\sqrt{5x}-5=0$

• A. True
• B. False

Answer 1

The correct option is A True

$3x^2+2\sqrt{5}x-5=0$

$\Rightarrow$ $3x^2+3\sqrt{5}x-\sqrt{5}x-5=0$

$\Rightarrow$ $3x(x+\sqrt{5})-\sqrt{5}(x+\sqrt{5})=0$

$\Rightarrow$ $(x+\sqrt{5})(3x-\sqrt{5})=0$

$\Rightarrow$ $x+\sqrt{5}=0$ and $3x-\sqrt{5}=0$

$\therefore$ $x=-\sqrt{5}$ and $x=\frac{\sqrt{5}}{3}$

$\therefore$ We can see roots given in question are correct.