Let p (x) be a polynomial of degree three that has a local maximum value 8 at x =1. and a local minimum value 4 at x = 2, then p (0) is equal to

# Let  be a polynomial of degree three that has a local maximum value 8 at . and a local minimum value 4 at , then is equal to

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### Solution:

We find that  is a quadratic polynomial having  and as its two zeros.

.where $\lambda$ is a positive constant.

..(i)

where $C$ is a constant .

It is given that  and .

Hence, $p\left(0\right)=C=-12$.

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