# Polynomial Functions Question Help (Urgent)

• Mar 24th 2009, 04:29 PM
Clueless
Polynomial Functions Question Help (Urgent)
I just can't get this question and need some help:

The equation 3x^3 + 25x^2 - 48x = -20 has roots of 1, h and k. Determine a quadratic equation f(x) whose roots are "h+k" and "hk". Present your final answer both in factored and expanded form.

• Mar 24th 2009, 04:34 PM
rtblue
Ok... Well, i might not even know how to do this problem, although i will give it a shot. I know the idea of what you have to do.

Equation:

\$\displaystyle 3x^3\oplus25x^2\ominus48x\oplus20\$

Here the objective is to factor this. This is what i shall attempt to do, you know that one of the roots is 1, so you plug that in automatically. I well get back to this post, and edit it, if i manage to factor this cubic -.- if i dont edit it, i didn't get it, and your on your own :(
• Mar 24th 2009, 04:51 PM
stapel
Quote:

Originally Posted by Clueless
The equation 3x^3 + 25x^2 - 48x = -20 has roots of 1, h and k.

Since one root is known, it can be divided out. So divide x - 1 from the polynomial 3x^3 + 25x^2 - 48x + 20.

Apply the Quadratic Formula to the resulting quadratic factor to find the other two zeroes. Name one of them "h" and the other one "k". (Wink)
• Mar 24th 2009, 05:15 PM
Clueless
Quote:

Originally Posted by stapel
Since one root is known, it can be divided out. So divide x - 1 from the polynomial 3x^3 + 25x^2 - 48x + 20.

Apply the Quadratic Formula to the resulting quadratic factor to find the other two zeroes. Name one of them "h" and the other one "k". (Wink)

oh thanks I divided it and then forgot what to use :)

So I got (x+1)(3x^2 + 22x - 70) - 50 = 3x^3 + 25x^2 - 48x + 20

So all I need to do is use the quadratic formula on 3x^2 + 22x - 70? Also after that the rest of the question just wants me to get "hk" and "h+k" and replace them as roots?

I'm not sure so just asking D:
• Mar 24th 2009, 05:28 PM
stapel
Quote:

Originally Posted by Clueless
I got (x+1)(3x^2 + 22x - 70) - 50 = 3x^3 + 25x2 - 48x + 20

How did you get this...?

Note: Since you're being asked to factor, rather than to break into terms, you need to divide the x - 1 (not "x + 1", since x = -1 is not given as a zero) into the polynomial provided earlier.

:D
• Mar 24th 2009, 05:48 PM
Clueless
Quote:

Originally Posted by stapel
How did you get this...?

Note: Since you're being asked to factor, rather than to break into terms, you need to divide the x - 1 (not "x + 1", since x = -1 is not given as a zero) into the polynomial provided earlier.

:D

I did synthetic division by negative 1 and got 3 , 22, -70 and also -50 as a remainder.

Also that's my division statement. Tell me if I did it wrong and what exactly the right answer is T_T
• Mar 24th 2009, 06:17 PM
skeeter
Quote:

Originally Posted by Clueless
I did synthetic division by negative 1 and got 3 , 22, -70 and also -50 as a remainder.

Also that's my division statement. Tell me if I did it wrong and what exactly the right answer is T_T

do synthetic division with 1. the root is x = 1, not -1.

you should get 0 as the remainder, right?