Form a polynomial fx with real coefficients having the given

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 5, multiplicity 2; 6i Enter the polynomial. f(x)=a(.) (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)

Solution

zeros are 5 ( multiplicity 2 )

6i

complex zeros occur in pair so if 6i is one zero other would be -6i

let f(x) = a( x- x1 )(x-x2) (x-x3)

where x1 and x2 are teh zeros

plugging the values we get

f(x) = a( x-5)^2 (x-6i)(x+6i)

f(x) = a( x^4-10x^3+61x^2-360x +900)