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# Find all the real zeros of the polynomial

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Find all the real zeros of the polynomial

p(x)=x^3 + x^2-3x+1

Apr 7, 2020

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By the rational root theorem, we can see that one(1) is root.

Now, create a synthetic division chart.

-1 |_1__1___-3____1_

This leaves us with the polynomial: x^2 + 2x - 1=0

Here, we can use the quadratic formula to get: $$x_1=-1+\sqrt{2}, x_2=-1-\sqrt{2}$$.

Thus, the roots of the equation p(x)=x^3+x^2-3x+1 are $$x_1=1, x_2=-1+\sqrt{2}, x_3=-1-\sqrt{2}$$,

Apr 7, 2020