Question 664354: Need to find the x and y intercepts of a polynomial. Problem is f(x)=2(x-3)(x^2+4)^3. Trying to figure out how to solve please.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Need to find the x and y intercepts of a polynomial. Problem is f(x)=2(x-3)(x^2+4)^3
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f(x)=2(x-3)(x^2+4)^3
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The y-intercept is at x = 0
y-int = 2(-3)*(4)^3 = -384
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The x-intercepts are the zeroes of f(x)
Ignore the 2
For f(x) = 0, either (x-3) = 0 --> x = 3
or,
(x^2+4) = 0 --> x = +/- 2i
The 2i zeroes are complex, and don't cross the axis.
Only x = 3 is a real number solution that intercepts the x-axis.
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