Question

which of the following quartic functions has x=-2 and x=-3 as its only two real zeros

Answer 1

\[(x+2)(x+3)\cdot\mathrm{something}\]

Answer 2

Answers choices are here:
x4 – 5x3 + 7x2 – 5x + 6
x4 + 5x3 + 7x2 + 5x + 6
x4 + 5x3 + 7x2 – 5x – 6

x4 – 5x3 + 7x2 + 5x – 6

Answer 3

By Newton Formulas, you can deduce that it must be only the first or the second (2*3=6). But only the first is the correct because the term with x must be
\[-(x_1+x_2)\cdot x=-(2+3)x=-5x\]

Answer 4

You can also check it,
\[(x-x_1)(x-x_2)=x^2-(x_1+x_2)+x_1x_2\]

Answer 5

Thanks so much! I appreciate the help!

Answer 6

I think I can take it from here now. :)