SOLUTION: what are the positive zeros of f(x)=2x^4-9x^3+2x^2+21x-10?

Question 574517: what are the positive zeros of f(x)=2x^4-9x^3+2x^2+21x-10?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
what are the positive zeros of f(x)=2x^4-9x^3+2x^2+21x-10?
x = 1/2 & x = 2
--------------
Divide those out and solve the quadratic for the other 2, 1 is positive.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Rational zeros of a polynomial are fractions with only certain possible numbers for numerator and denominator. The numerator (m) must be a factor/divisor of the independent term (-10 in this case), so 1, 2, 5, and 10 are the only positive possibilities. The denominator (n) must be a factor of the leading coefficient of the polynomial (2 in this case), so 1, and 2 are the only positive possibilities. (The rational zero fractions can have a plus or minus sign, but we will look for only the positive ones).
Putting it all together, the only possible positive rational zeros are 1/2, 1, 2, 5/2, 5, and 10.

So far we have two positive zeros: 1/2 and 2.
That means the polynomial is divisible by and by .
So it must be divisible by
Dividing f(x) by , I got
, so
Solving any which way we can (quadratic formula or completing the square), we get any remaining zeros of f(x). We get

, so the positive zeros of f(x) are:
, , and .
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