# What are the possible number of positive real, negative real, and complex zeros of #f(x) = 4x^3 + x^2 + 10x – 14#?

##### 1 Answer

#### Answer:

This cubic has one Real zero and a Complex conjugate pair of non-Real zeros.

#### Explanation:

The signs of the coefficients follow the pattern:

With one change of sign, we can tell that this cubic polynomial has one positive zero.

Consider

#f(-x) = -4x^3+x^2-10x-14#

The signs of the coefficients follow the pattern:

With two changes of sign, we can tell that this cubic has

Let us examine the discriminant:

This has discriminant

#Delta = b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd#

#=100-16000+56-84672-10080#

#=-110596#

Since

graph{4x^3+x^2+10x-14 [-10, 10, -200, 200]}