Question

the quadratic equation whose roots are -2,-3√2​

Answer 1

      $\bold{Answer:}$

      $\boxed{x^{2} +(2+3\sqrt2)x + 6\sqrt2 = 0}$

      $\bold{Step-by-step}$  $\bold{explaination}$

      $\text{The given roots are }-2,-3\sqrt{2}$

       $\text{We know that a quadratic equation is of the form }\\x^{2} -(\text{Sum of roots})x + (\text{Product of roots})$

$\implies \text{Sum of roots} = -2+(-3\sqrt{2}) = -(2+3\sqrt{2})$

$\implies \text{Product of roots} = (-2)(-3\sqrt{2}) = 6\sqrt{2}$

$\implies \text{The quadratic equation} = x^{2} -[-(2+3\sqrt2)]x + 6\sqrt2$

                                        $\implies x^{2} +(2+3\sqrt2)x + 6\sqrt2 = 0$