Question

Find the roots of the equation, and check them using the Vieta's theorem: x^2−15x−16=0

Answer 1

The roots are fairly simple to find, no need to invoke quadratic formula. First we factor,

$x^2-15x-16=0\implies (x-16)(x+1)=0$

Then we get zeros at $x_1=16,x_2=-1$.

Using veita's formulas we can check it namely,

$

x_1x_2=c/a\implies 16(-1)=-16/1\implies -16=-16\\

x_1+x_2=-b/a\implies 16-1=-(-15/1)\implies 15=15

$

So as you can see solutions pass both tests and therefore are valid.

Hope this helps.