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=-(12)/(8)=-(3)/(2) \end{gathered}`

The root is

`-(3)/(2)`

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

`(v+(3)/(2))^2=0`

or

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