Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 
4, -14, and 5 + 8i

misty1212 · Answer

HI!!

misty1212 · Answer

first start out by writing the two easy factors
it is clear that if one of the zeros is 4 then one factor is $x-4$?

anonymous · Answer

Okay  so the factors would be x-4, x+14, x-(5+8i), x- (5-8i)?

misty1212 · Answer

yes, and it is easy to multiply out $(x-4)(x+14)$ but it is harder to multiply out the last two
there is however an easier way to find the quadratic with zeros $5\pm 8i$

misty1212 · Answer

actually there are two easy ways, one is easy, one is real real easy, but the real real easy way requires memorizing something so if you are going to to only one or two the easy way might be preferable 
you pick

anonymous · Answer

Can we do the on that requires memorization? Itd probably help more in the long run

misty1212 · Answer

ok sure
if a zero of a quadratic is $a+bi$ then the quadratic is $$x^2-2ax+(a^2+b^2)$$

misty1212 · Answer

in your case $a=5,b=8$

misty1212 · Answer

so what do you get for $$(x-(5+8i))(x-(5-8i))$$ doing it the real quick way?

anonymous · Answer

X^2 -10x + 89?

anonymous · Answer

Then do I multiply that with the foil of (x-4)(x+14)?

perl · Answer

correct

perl · Answer

(x^2 -10x + 89)(x-4)(x+14)?