Question

Polynomial of lowest degree with zeros of 3/4 (multiplicity 2) and 1/3 (multiplicity 1) and with f(0) = -81

Answer 1

The polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .

What is a Polynomial ?

A polynomial is an expression that consists of indeterminate , Coefficients , exponents and mathematical operations.

It is given that

The zero of the function is at 3/4 with multiplicity of 2 = (x - 3/4)²

The zero of the function is at 1/3 with multiplicity of 1 = (x - 1/3)

The polynomial can be written as

f(x) = a (4x − 3)² (3x - 1)

-81 = a (0 − 3)² (0 -1)

a = 9

f(x) = 9(4x − 3)² (3x - 1)

Therefore the polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .

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