How can I ...?

Question

How do I determine the equation of the quadratic function with roots 2 + i and 2 - 1

How do I determine the zeros of
p(x) = (x^2 -x -2)(x^2 + 2x - 15)

Answer 1

For the first problem, the equation is

(x-(2+i))*(x-(2-1)) = 0

or

x^2 - (3+i)*x + (2+i) =0

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For the second problem you just need to determine the zeros of each second-order polynomial, which in this case are:

x = -1
x = +2
x = +3
x = -5

I hope this helps.

Answer 2

Well K that is 2 questions, I hope the answers fit here...the quadratic function with root 2+i and 2-1 is sort of a trick question, but the basic foil technique is still sound. foil = (F)irst, (O)uter, (I)nner, (L)ast. Multiply the first values, outer values, inner then the last and add them all together. that would be 4, -2, 2i, and -i. Add them all together and you get 2+i. Notice that that is one of the roots of the equation! That is why I said it was a trick question. Since the 2nd root had no variable (i) it doesn't matter at all. Next time you see a question like that just ignore ALL roots with no variable.

karlterzaghi did a great job of answering the second question...best of luck to you

Answer 3

(2+i) (2-i)
2(2-i)+i(2-i)
4 - 2i + 2i - i^2
4 - i^2 <--------answer


you solve for x to determine the zeros
p(x) = (x-2)(x+1)(x+5)(x-3)
x-2 = 0 x+1 = 0 x+5 = 0 x-3 = 0
x = 2 x = -1 x = -5 x = 3