I’ll give Brainly! Match each problem with the answer!
2 answers:
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Answer:
Choice b.
.
Step-by-step explanation:
The highest power of the variable in this polynomial is
. In other words, this polynomial is quadratic.
It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to .)
After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.
Apply the quadratic formula to find the two roots that would set this quadratic polynomial to . The discriminant of this polynomial is
.
.
Similarly:
.
By the Factor Theorem, if is a root of a polynomial, then
would be a factor of that polynomial. Note the minus sign between
and
.
- The root
corresponds to the factor
, which simplifies to
.
- The root
corresponds to the factor
, which simplifies to
.
Verify that indeed expands to the original polynomial:
.
The roots or zeros of a polynomial are the points it crosses the x-axis.
The roots of the polynomial in order from least to greatest are -5, 0 and 5
From the graph (see attachment), we have the following highlights
- <em>The graph cross the x-axis at x = -5</em>
- <em>The graph cross the x-axis at x = 0</em>
- <em>The graph cross the x-axis at x = 5</em>
The points at which the graph crosses the x-axis are the roots of the graph.
So, the roots are: -5, 5 and 5
Read more about the roots of a polynomial at:
