select the correct answer from the drop - down menu. find the polynomial. {5} is the solution set of x^2…

select the correct answer from the drop - down menu. find the polynomial. {5} is the solution set of x^2 - 5x + 25 = 0; x^2 + 10x + 25 = 0; x^2 - 10x + 25 = 0; x^2 + 5x + 25 = 0

select the correct answer from the drop - down menu. find the polynomial. {5} is the solution set of x^2 - 5x + 25 = 0; x^2 + 10x + 25 = 0; x^2 - 10x + 25 = 0; x^2 + 5x + 25 = 0

Answer

Explanation:

Step1: Recall zero - factor property

If (x = a) is a solution of a polynomial equation, then ((x - a)) is a factor of the polynomial. Since the solution set is ({5}), the polynomial has a factor ((x - 5)) and the polynomial is ((x - 5)(x - 5)=x^{2}-10x + 25). We can also check by substituting (x = 5) into each polynomial.

Step2: Substitute (x = 5) into (x^{2}-5x + 25)

When (x = 5), (5^{2}-5\times5 + 25=25-25 + 25=25\neq0).

Step3: Substitute (x = 5) into (x^{2}+10x + 25)

When (x = 5), (5^{2}+10\times5 + 25=25 + 50+25 = 100\neq0).

Step4: Substitute (x = 5) into (x^{2}-10x + 25)

When (x = 5), (5^{2}-10\times5 + 25=25-50 + 25=0).

Step5: Substitute (x = 5) into (x^{2}+5x + 25)

When (x = 5), (5^{2}+5\times5 + 25=25+25 + 25=75\neq0).

Answer:

(x^{2}-10x + 25 = 0)