# Math Help - Polynomial Functions Gr 12- Thinking and Inquiry Question

1. ## Polynomial Functions Gr 12- Thinking and Inquiry Question

I have two Questions:

any sort of help would help even a hint of what methods to use much appreciated

i just need help with 1 of the 2 questions which ever is easier
The reason i put 2 questions up is because one is copied of the board not sure if i copied it right other one is given from my text with the solution.

1.)

f(x)= 3x^3+b^2+cx+2

Zeros (x-2) (x+3)

solve for b and c

2.)

f(x)= 3x^4 +14x^3+px^2+qx+24 has x intercepts -4 and 2
determine the function

Solution: f(x)= 3x^4+14x^3-11x^2-70x+24

2. Originally Posted by s.a.n.t.a.n.a
I have two Questions:

any sort of help would help even a hint of what methods to use much appreciated

i just need help with 1 of the 2 questions which ever is easier
The reason i put 2 questions up is because one is copied of the board not sure if i copied it right other one is given from my text with the solution.

1.)

f(x)= 3x^3+bx^2+cx+2

Zeros (x-2) (x+3)

solve for b and c
Are you missing an x at the place where I inserted it?

When y=0, the function crosses the x-axis; these are the zeros.

So (x-2) is a zero, and so is (x+3). This implies that $x-2=0\implies x=2$ and $x+3=0\implies x=-3$

So plugging these two x values into the function, we should see that

$3(2)^2+b(2)^2+c(2)+2=0\implies 4b+2c=-14\implies 2b+c=-7$

$3(-3)^2+b(-3)^2+c(-3)+2=0\implies 9b-3c=-29$

Can you solve this system of equations?

$\left\{\begin{array}{rcrcr}2b&+&c&=&-7\\9b&-&3c&=&-29\end{array}\right.$

2.)

f(x)= 3x^4 +14x^3+px^2+qx+24 has x intercepts -4 and 2
determine the function

Solution: f(x)= 3x^4+14x^3-11x^2-70x+24
This one follows the same idea as the previous problem. Plug these two values into the function, noting that when x=-4 and 2, f(-4)=f(2)=0. Then solve the system of equations.

Can you take it from here?

--Chris

3. Ya i see what you did there but im still not sure how to solve for b c
and i am not sure were you got the negitive 1 from