SirSnapple SirSnapple
  • 04-04-2020
  • Mathematics
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Find the roots of the equation, and check them using the Vieta's theorem: x^2−15x−16=0

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r3t40
r3t40 r3t40
  • 04-04-2020

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

[tex]x^2-15x-16=0\implies (x-16)(x+1)=0[/tex]

Then we get zeros at [tex]x_1=16,x_2=-1[/tex].

Using veita's formulas we can check it namely,

[tex]

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

[/tex]

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

Hope this helps.

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