Math CentralQuandaries & Queries


Question from Dakota, a student:

My problem has multiple steps and I have done everything but the last one. The original problem is f(x)=x^4-5x^3+7x^2+3x-10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^3-3x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it.

Hi Dakota,

I assume you used substitution to find a zero of $f(x),$ say $x = a,$ and then you divided $f(x)$ by $x - a$ to arrive at the cubic equation. You should check your work. You didn't tell us what zero you found but I think there is an error in your division. If you correct your error then you can use the same procedure again on the resulting cubic.


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