How do you use the rational roots theorem to find all possible zeros of $f (x) = x^{3} + 10 x^{2} - 13 x - 22$ $f(x)=x^3+10x^2-13x-22$ ?

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How do you use the rational roots theorem to find all possible zeros of $f (x) = x^{3} + 10 x^{2} - 13 x - 22$ $f(x)=x^3+10x^2-13x-22$ ?

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Answer 1 · 2016-06-05T23:15:24

$x = - 1$ $x = -1$ , $x = 2$ $x=2$ and $x = - 11$ $x=-11$

Explanation:

$f (x) = x^{3} + 10 x^{2} - 13 x - 22$ $f(x) = x^3+10x^2-13x-22$

By the rational root theorem, any rational zeros of $f (x)$ $f(x)$ must be expressible in the form $\frac{p}{q}$ $p/q$ for integers $p, q$ $p, q$ with $p$ $p$ a divisor of the constant term $- 22$ $-22$ and $q$ $q$ a divisor of the coefficient $1$ $1$ of the leading term.

That means that the only possible rational zeros are:

$\pm 1$ $+-1$ , $\pm 2$ $+-2$ , $\pm 11$ $+-11$ , $\pm 22$ $+-22$

Trying each in turn, we find:

$f (- 1) = - 1 + 10 + 13 - 22 = 0$ $f(-1) = -1+10+13-22 = 0$

$f (2) = 8 + 40 - 26 - 22 = 0$ $f(2) = 8+40-26-22 = 0$

$f (- 11) = - 1331 + 1210 + 143 - 22 = 0$ $f(-11) = -1331+1210+143-22 = 0$

So we have found all of the zeros:

$x = - 1$ $x = -1$ , $x = 2$ $x=2$ and $x = - 11$ $x=-11$

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How do you use the rational roots theorem to find all possible zeros of $f (x) = x^{3} + 10 x^{2} - 13 x - 22$ $f(x)=x^3+10x^2-13x-22$ ?

1 Answer

Explanation:

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Science

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How do you use the rational roots theorem to find all possible zeros of f(x)=x3+10x2−13x−22f(x)=x^3+10x^2-13x-22 ?

1 Answer

Explanation:

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How do you use the rational roots theorem to find all possible zeros of $f (x) = x^{3} + 10 x^{2} - 13 x - 22$ $f(x)=x^3+10x^2-13x-22$ ?