Question

Please Help!!! WILL GIVE BRAINLIEST!!!

Answer 1

Answer:

The correct statements are:

A) This polynomial has a degree of 2, so the equation $x^{2} + 4x + 4$has exactly two roots.

B: The quadratic equation $x^{2} + 4x + 4$ has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

Step-by-step explanation:

Here, the given polynomial is  $f(x) = x^{2} + 4x + 4$

FUNDAMENTAL THEOREM OF ALGEBRA:

If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

Now, here the given polynomial is a quadratic polynomial with degree 2.

So, by the fundamental theorem, f(x) has EXACTLY 2 roots including multiple and complex roots.

Now, solving the equation , we get that the only possible roots of the polynomial p(x) is x = -2 and x = -2

So, f(x) has only one distinct root x = -2 with a multiplicity 2.

Hence, the correct statements are:

A) This polynomial has a degree of 2, so the equation $x^{2} + 4x + 4$has exactly two roots.

B: The quadratic equation $x^{2} + 4x + 4$ has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.