Question

What polynomial has roots of -6, 1, and 4 ?

Answer 1

a) x3 - 9x2 - 22x + 24
b) x3 - x2 - 26x - 24
c) x3 + x2 - 26x + 24
d) x3 + 9x2 + 14x - 24

Answer 2

The roots are the solutions to \(ax^3+bx^2+cx+d=0\) so if you put the roots back in to \((x-n)\) form, you can multiply them ans have the answer.

Answer 3

what do i multiply?

Answer 4

You have -6, 1, and 4. That means, x=-6, x=1, and x=4. Well, turn that back into three \(x\pm n=0\) things. Then take all three \(x\pm n\) parts as factors and multiply them.

Answer 5

sorry im lost

Answer 6

If I say x+2=0, solve for x, you do:
\(x+2-2=-2 \implies x=-2\).

So do that in reverse to change all three of your -6, 1, and 4 into factors.

Answer 7

Another way to say it is, solve these for zero:
\(\begin{align*}
x&=-6\\
x&=1\\
x&=4
\end{align*}\)

Answer 8

okay?

Answer 9

i got answer c was i correct

Answer 10

Yep!

Answer 11

wait are you serious?

Answer 12

\((x+6)(x-1)(x-4) = x^3+x^2-26x+24\)

Answer 13

thanks!

Answer 14

np. Have fun!