Answer:
The solutions and the x-intercepts of the polynomial are:
Step-by-step explanation:
Given a function <em>f</em> a solution or a root of <em>f</em> is a value at which
.
An x-intercept is a point on the graph where y is zero.
To find the solutions of the polynomial and the x-intercepts you need to:
First, we need to factor the polynomial expression
Factor the common term
We can treat as a quadratic function with respect to
Let . We can rewrite
in terms of
as follows:
We need to solve the quadratic equation
for this we can use the Quadratic Equation Formula:
For a quadratic equation of the form the solutions are
the solutions to the quadratic equation are:
Therefore,
Recall that so
Using the Zero factor Theorem: If ab = 0, then either a = 0 or b = 0, or both a and b are 0.
roots are
;
roots are
;
The solutions and the x-intercepts are:
Because all roots are real roots the x-intercepts and the solutions are equal.