algebra
posted by Pat
Using the rational zeros theorem to find all zeros of a polynomial
The function below has at least one rational zero. Use this fact to find all zeros of the function
h(x)=7x^49x^341x^2+13x+6
if more than one zero, separate with commas. Write exact values, not decimal approximations

Reiny
I tried factors of 6 and found
f(2)=0 and f(3) =0
so after successive synthetic divisions I had the factors,
(x+2)(x3)(7x^2  2x  1)
solving (x+2)(x3)(7x^2  2x  1) = 0
x = 2, 3, or (2 ±√32)/14
= 2, 3, or (1 ± 2√2)/7
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