Question

Find the potential real zeros (roots) of the following equation.

f(x) = 4x5 - 16x4 + 17x3 - 19x2 + 13x - 3 = 0

Answer 1

I do not believe this is the right question. Are you SURE it's not the "potential RATIONAL zeros"?

Answer 2

@tkhunny they might have meant that

Answer 3

The rational root theorem is easily understood with a linear factor.

If we have 3x-5 = 0, the solution is x = 5/3. What is important for this discussion is that 5 (numerator) comes from the constant terms and 3 (denominator) comes from the leading coefficient. This is the general idea.

You have a constant term of 3 and a leading coefficient of 4. This means, IF you have a rational zero, it MUST look like this: \(x = \dfrac{factor\;of\;3}{factor\;of\;4}\). Can you list them all?