Question

Find a polynomial of least possible degree having the graph shown f(x)=0

Answer 1

The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.

Polynomial of least possible degree

It follows from the graph that the roots of the polynomial are; -2, 3 and 7.

On this note, the factors of such polynomial are;

Hence; (x+2)(x-3)(x-7) = f(x)

• f(x) = x³-8x²+x +42

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