Question

A fifth-degree polynomial factored over the integers is: p(x)=3x(x-2)(5x-7)(x^2-4x+8)
How many zeros are real?
How many zeros are non real?

Answer 1

You know that at least 3 zeroes are real since you've factored the polynomial into 3 linear terms and 1 quadratic. The linear terms each represent a single real zero.

This means we need to find how many real/complex roots the quadratic has.

Answer 2

To do this, you'll want to look at the discriminant \(b^2-4ac\). If we calculate this, we get\[b^2-4ac=16-4(8)=-16\]Since this is negative, we must have two complex zeroes.

Answer 3

what is the difference between a real zero and a complex zero?

Answer 4

A complex zero is a zero that looks like the form \(a+bi\) where \(i=\sqrt{-1}\)

Answer 5

so it is not real?

Answer 6

correct

Answer 7

so that means it has 3 real zeros and 2 non real zeros?

Answer 8

That is correct.

Answer 9

thanks

Answer 10

You're welcome.