write a polynomial of least degree with roots -9 and -3. write your answer using the variable x and in…
write a polynomial of least degree with roots -9 and -3. write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer
Explanation:
Step1: Use factor - root relationship
If (r) is a root of a polynomial, then ((x - r)) is a factor. Given roots (r_1=-9) and (r_2 = - 3), the factors are ((x+9)) and ((x + 3)).
Step2: Multiply the factors
((x + 9)(x + 3)=x\times x+x\times3+9\times x + 9\times3) (=x^{2}+3x+9x + 27) (=x^{2}+12x + 27)
Answer:
(x^{2}+12x + 27)