SOLUTION: The function f is defined by {{{f(x)=3x^3-2x^2+cx}}}, where c is a constant. The graph of f has three x-intercepts in the xy-plane.They are the points{{{(-1/3.0)}}}, (1,0),and(p,0)

Algebra ->  Functions -> SOLUTION: The function f is defined by {{{f(x)=3x^3-2x^2+cx}}}, where c is a constant. The graph of f has three x-intercepts in the xy-plane.They are the points{{{(-1/3.0)}}}, (1,0),and(p,0)      Log On


   

Question 1041286: The function f is defined by f%28x%29=3x%5E3-2x%5E2%2Bcx, where c is a constant. The graph of f has three x-intercepts in the xy-plane.They are the points%28-1%2F3.0%29, (1,0),and(p,0).What is the value of p?
A)1
B)1%2F3
C)-1%2F3
D)0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=3x%5E3-2x%5E2%2Bcx
f%28x%29=x%2A%283x%5E2-2x%2Bc%29 Factor out the GCF x
0=x%2A%283x%5E2-2x%2Bc%29 Replace f(x) with 0
x%2A%283x%5E2-2x%2Bc%29=0 Flip the equation


Since x%2A%283x%5E2-2x%2Bc%29=0, this means that x+=+0 or 3x%5E2-2x%2Bc

Since one root is x+=+0, this means that one x-intercept is the ordered pair (x,y) = (0,0)

The only thing that comes close to that is (p,0) which is listed above.

(p,0) = (0,0)
means p = 0

So the final answer is choice D) 0