Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

3, –13, and 5 + 4i

show me steps

Answer 1

well, you have the real zeroes, so creating those factors is straightforward , e.g x=3 so one factor is (x-3)

Answer 2

for the complex zero, remember that there is going to be a conjugate of that , 5+4i, and 5-4i, so that's two more zeroes

Answer 3

Then you can arrange all of them to form your equation
f(x) = (x-?)(x-?)(x-?)(x-?) to generate a polynomial

Answer 4

how do you write it?

Answer 5

do you have all the factors worked out? If so , then you just need to multiply the factors to get apolynomial in std form, i.e ax^4+ax^3...etc

Answer 6

since 3 is a zero, (x-3) will be a factor of polynomial

Answer 7

since -13 is a zero, (x+13) will be another factor of the required polynomial

Answer 8

so can we write the polynomial wid zeroes of 3 and -13 as,

f(x) = (x-3)(x+13)

?

Answer 9

@sara1234 does that make sense

Answer 10

oh nice victor hugo ! you studying french poetry :)