Write a Function For This Polynomial

• Oct 7th 2007, 02:18 PM
DesiKid89
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.
• Oct 7th 2007, 02:25 PM
Jhevon
Quote:

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: \$\displaystyle P(x) = (x + 2)(x + 1)(x - 5)^2\$

now expand
• Oct 7th 2007, 03:33 PM
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)?
• Oct 7th 2007, 03:40 PM
Jhevon
Quote:

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 \$\displaystyle P(x) = -(x + 2)(x + 1)(x - 5)^2\$
• Oct 7th 2007, 04:01 PM
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.
• Oct 7th 2007, 04:45 PM
Jhevon
Quote:

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?? (Nerd)