How do you find the roots of $x^3+x^2-17x+15=0$ ?

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Answer 1 · 2016-09-23T21:12:33

The roots are: $x=1$ , $x=-5$ and $x=3$

$x^3+x^2-17x+15 = 0$

Note that the sum of the coefficients is $0$ . That is:

$1+1-17+15 = 0$

So $x=1$ is a root and $(x-1)$ a factor:

$0 = x^3+x^2-17x+15$

$color(white)(0) = (x-1)(x^2+2x-15)$

Then note that $5*3=15$ and $5-3=2$ , so

$x^2+2x-15 = (x+5)(x-3)$

So the other two roots are $x=-5$ and $x=3$

How do you find the roots of x^3+x^2-17x+15=0x^3+x^2-17x+15=0?