Precalculus · Problem 51

Rational Functions — Stitz & Zeager

Mathematics — Precalculus · constructing-polynomial-from-zeros

Problem

Create a polynomial

f

with real number coefficients which has all of the desired characteristics. You may leave the polynomial in factored form. • The solutions to

f(x) = 0

are

x = \pm 2

and

x = \pm 7i

• The leading term of

f(x)

-3x^5

• The point

(2, 0)

is a local maximum on the graph of

y = f(x)