Question

What is the expression in factored form?x^2+13x+14

Answer 1

Answer:

$\left(x-\dfrac{-13+\sqrt{113}}{2}\right)\left(x-\dfrac{-13-\sqrt{113}}{2}\right).$

Step-by-step explanation:

To factor the expression $x^2+13x+14$ you need to know its roots.

First find the discriminant of this quadratic polynomial:

$D=13^2-4\cdot 1\cdot 14=169-56=113.$

Then the roots of the expression $x^2+13x+14$ are

$x_{1,2}=\dfrac{-13\pm \sqrt{113}}{2}.$

Now the factored form is

$\left(x-\dfrac{-13+\sqrt{113}}{2}\right)\left(x-\dfrac{-13-\sqrt{113}}{2}\right).$