Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: $f (x) = 2 x^{3} - 9^{2} + 10 x - 3$ $f(x)=2x^3-9^2+10x-3$ ?

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Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: $f (x) = 2 x^{3} - 9^{2} + 10 x - 3$ $f(x)=2x^3-9^2+10x-3$ ?

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Answer 1 · 2016-02-27T00:20:49

First, I always like to start off the rational root theorem by using x = 1.
This is because it is very easy to quickly count a possibility: just count the coefficients.

So we do $2 - 9 + 10 - 3$ $2 - 9 + 10 - 3$

And from there we were able to quickly find a root, $x = 1$ $x = 1$

Now, we just synthetically divide

x1 2 -9 10 -3
2 -7 3
Result 2 -7 3 0

So now, after dividing by $x - 1$ $x-1$ , we have $2 x^{2} - 7 x + 3$ $2x^2 - 7x + 3$

If you see the factors, you can just factor it. Otherwise, use the quadratic formula

$\frac{7 \pm \sqrt{49 - 24}}{4}$ $(7 +- sqrt(49 - 24))/4$

$\frac{7 \pm 5}{4}$ $(7 +-5)/4$

So we have either 3 or 1/2.

Do not forget the $x = 1$ $x=1$ that we already found, and we have zeroes at 1/2, 1, and 3

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Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: $f (x) = 2 x^{3} - 9^{2} + 10 x - 3$ $f(x)=2x^3-9^2+10x-3$ ?

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Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: f(x)=2x3−92+10x−3f(x)=2x^3-9^2+10x-3?

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Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: $f (x) = 2 x^{3} - 9^{2} + 10 x - 3$ $f(x)=2x^3-9^2+10x-3$ ?