Information is given about a polynomial fx whose coefficient

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 3; zeros: - 6, - 5 - i Enter the remaining zeros of f.

Solution

Given

Degree of the polynomial is 3

and zeros -6 , (-5 -i)

we can see that (-5 -i) is a complex number (as \"i\" is present in that term)

and (-5 -i) is a root of the polynomial, complex roots always exists in pair.

so the other root is the conjugate of this complex number

for finding conjugate we reverse the sign of \"i\"

so the other root is   \"-5 + i\"

degree = 3 means , this polynomial will have 3 roots

so the roots are -6, (-5 -i) and (-5 +i)