MOTI www.mathxl.com/Student/PlayerHomework.aspx MAC1147 PRECAL/TRIG M T w R 11.0

Question

MOTI www.mathxl.com/Student/PlayerHomework.aspx MAC1147 PRECAL/TRIG M T w R 11.00 AM 12:15 PM CHRISTIE HEINRICHSTS979- usI Homework: Section 3.4-Fall 2017 es Score: 0 of 1 pt orme 3.4.27 16 or 18 (17 complete) HIV Score: 8704%, 1567 of 18 p Question Hep * , Find an nth-degree polynomial function with real coefficients satisfying the given conditions If you are using a graphing utlity, use i to graph the function and venfy the Testsreal zeros and the given function value n=3; -3 and 6+4 i are zeros: f (1)= 164 f(x) Type an expression using x as the variable Simplifty your answer) onten ucce ucce Libra

Explanation / Answer

Given :

-3 , 6 - 4i are zeros of polynomial equation of degree = 3

Imaginary roots occur in conjucate pairs.

So,

If (6 - 4i ) is root then (6 + 4i) will also be root of polynomial.

Therefore polynomial will be

f(x) = (x + 3)(x - (6 + 4i))(x - (6 - 4i))

f(x) = (x + 3)(x - 6 - 4i)(x - 6 + 4i)

Verify f(1) = 164

f(1) = (4)(-5 - 4i)(-5 + 4i)

= (4)(25 + 16)

= (4)(41)

= 164

Hence verified.

f(x) = (x + 3)(x - 6 - 4i)(x - 6 + 4i)

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