Question

How many negative roots will this function have? f(x) = x^7 – 2x^4 + 7x^2 + 2x – 2 help plsss

Answer 1

There are two negative roots to the provided polynomial function

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

$\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n$

We have a polynomial function:

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

$\rm f(x) =\left(x+1\right)\left(x^6-x^5+x^4-3x^3+3x^2+4x-2\right)$

Using the zero product property:

$\rm \left x+1\right = 0 \ \ \ or \left x^6-x^5+x^4-3x^3+3x^2+4x-2\right = 0$

After solving:

x = -1, x = -0.853, and x = 0.418 (using the graph method)

Thus, there are two negative roots to the provided polynomial function

f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

Learn more about Polynomial here:

brainly.com/question/17822016

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