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Answer:
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.