# Thread: Polynomial Functions Question Help (Urgent)

1. ## 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.

2. 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

3. 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".

4. 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".
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:

5. 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.

6. 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.

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

7. 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?