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icang [17]
3 years ago
6

Determine the equation of the polynomial, p(x),in both factored and standard form.

Mathematics
1 answer:
melamori03 [73]3 years ago
4 0

We can see that the graph touches x=-1 without crossing the x-axis (i.e. it is a double solution), and then there's another zero at x=2 (this time it's a crossing zero, so a single solution).

This leads, up to multiple, to the polynomial

p(x)=a(x+1)^2(x-2)

If we impose the passing through (0,4) we have

p(0)=4=a(1)(-2) \iff -2a=4 \iff a=-2

So, the polynomial is

p(x)=-2(x+1)^2(x-2)=-2 x^3 + 6 x + 4

Finally, to solve p(x), simply look at the graph, searching for the points, where the graph is below the x-axis. You can see that this happens only if x>2, so that's the solution to your question.

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