Question

Find a polynomial function p which satisfies following criteria?

Answer 1

Answer:

p(x) has a double root at x = -4, and

a single root at x = 6. So the polynomial

has the form p(x) = a(x + 4)^2(x - 6) = ax^3 + . . . - 96a

But since p(x) ---> ∞ as x ---> - ∞ and ---> -∞ as x ---> ∞,

a must be < 0. That, together with the fact that p(0) = 1,

means a = - 1 / 96. So, p(x) = (- 1 / 96)(x + 4)^2(x - 6)

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