Thread: Write a Function For This Polynomial

Draw the graph and write a function for the polynomial that fits the following description.

p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

P(X)= _____________________




Can someone please help me with this problem? I'd really appreciate it. Thank you in advance.

Originally Posted by DesiKid89

Draw the graph and write a function for the polynomial that fits the following description.

p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

P(X)= _____________________




Can someone please help me with this problem? I'd really appreciate it. Thank you in advance.

try drawing axis with the intervals given. by marking the intervals where the graph is positive and/or negative (with say a tick for positive and an x for negative) you would realize that the zero x = 5 is a double root.

thus we have:

now expand

Ok, I expanded it out and I ended up with:

P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?

Originally Posted by DesiKid89

Ok, I expanded it out and I ended up with:

P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?

it should be a +55x here. but there is something else wrong. we need a negative x^4 graph to fulfill the conditions. so multiply through by -1 (after you fix the sign on the 55x)

so in short, you must find

Yeah now I got:

P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

...and that was right, thanks a lot man. Your like my new math idol, lol.

Originally Posted by DesiKid89

Yeah now I got:

P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

...and that was right, thanks a lot man. Your like my new math idol, lol.

you're welcome... you had a math idol??