Question

Factoring PolynomialsFind the roots of a quadratic equation with leading coefficient greater than 1

Answer 1

$4v^2+12v+9=0$

on this point we can use the formula to factor

$v=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

where a is 4, b is 12 and c is 9

replacing

$v=\frac{-(12)\pm\sqrt[]{(12)^2-4(4)(9)}}{2(4)}$

and solving

$\begin{gathered} v=\frac{-12\pm\sqrt[]{144-144}}{8} \\ \\ v=\frac{-12\pm\sqrt[]{0}}{8} \\ \\ v=-\frac{12}{8}=-\frac{3}{2} \end{gathered}$

The root is

$-\frac{3}{2}$

then the polynomial has one root -3/2 if we rewrite the polynomial is

$(v+\frac{3}{2})^2=0$

or

$(2v+3)^2=0$