Posted by Destiny on Tuesday, October 21, 2008 at 11:08pm.
HELP!!!!!!!!!!!!!
write equation of a polynomial function with the given characteristics.
Leading coefficient is 1 or 1
crosses the x axis at 2,3, and 4
touches the x axis at 0
lies above the x axis between 2 and 0

algebra  Reiny, Tuesday, October 21, 2008 at 11:26pm
from "touches the x axis at 0", we can see a double root of x=0 at the origin, meaning the curve must touch the xaxis at the origin without crossing.
But it does cross at x = 2,3 and 4
so we would have
y = ±1(x^2)(x+2)(x3)(x4)
[think of the x^2 as (x0)(x0)]
make a sketch with intercepts as I have indicated, having the curve rise to infinity in the 1st, and to negative infinity in the 3rd quadrants,
for the curve to be above the xaxis between 2 and 0
so the coefficient has to be +1
so y = (x^2)(x+2)(x3)(x4)
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