Will give !

use the quadratic polynomial x2+4x+4 to answer the questions.

a: which summary correctly applies the fundamental theorem to the quadratic polynomial?

b: which statement correctly verifies the application of the fundamental theorem of algebra?

select one answer for question a, and select one answer for question b.

a: this polynomial has a degree of 2, so the equation x2+4x+4=0 has exactly two roots.

a: this polynomial has a degree of 2, so the equation x2+4x+4=0 has two or fewer roots.

a: this polynomial has a degree of 2, so the equation x2+4x+4=0 has more than two roots.

b: the quadratic equation x2+4x+4=0 has two real solutions, x=−2 or x=2, and therefore has two real roots.

b: the quadratic equation x2+4x+4=0 has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

b: the quadratic equation x2+4x+4=0 has three real solutions, x=2, x=−2, and x=0, and therefore has three real roots. primary source: zimmermann telegram (links to an external site.)links to an external site.

The correct statements are:

A) This polynomial has a degree of 2, so the equation has exactly two roots.

B: The quadratic equation 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  

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 has exactly two roots.

B: The quadratic equation has one real solution, x=−2, and therefore has one real root with a multiplicity of 2.

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step-by-step explanation: