15 POINTS!!!!! !!!!!! could i have some help on #39 with an explanation?? i just really don’t get it, lol. i thought i did, but
then i looked at the answer key, and it is NOT what i thought. thank you guys so much, and happy halloween!!
1 answer:
Hey there! In this problem, the solutions, both real and imaginary are provided. We have to work backwards to create a polynomial function which matches these solutions:
f(x) = (x - 6), (x + [5 + 2i]), (x + [5 - 2i])
Create a difference of squares,
f(x) = (x - 6), ([x + 5] + 2i), ([x + 5] - 2i)
f(x) = (x - 6), ([x + 5]^2 + 4)
[(x + 5)(x + 5)] + 4
x^2 + 5x + 5x + 25 + 4
x^2 + 10x + 29
f(x) = (x-6), (x^2 + 10x + 29)
f(x) = x^3 + 10x^2 + 29x - 6x^2 - 60x - 174
Combine like terms,
f(x) = x^3 + 4x^2 + 29x - 174
There we have our answer, a polynomial of degree 3.
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