Question

Form the quadratic equation from the roots given below.
$1-3\sqrt{5}$ and $1+3\sqrt{5}$

Answer 1

Roots $=1-3\sqrt{5},1+3\sqrt{5}$

$\alpha +\beta =\frac{-b}{a}=2$

$\alpha \beta =(1-3\sqrt{5})(1+3\sqrt{5})$

$=1-3\left(5\right)=-14=\frac{c}{a}$

Equation $\Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}$

$\Rightarrow x^2-2x-14=0$.