Solving and Writing Polynomial Equations

Write a polynomial function of least degree with integral coefficients that has the given zeros.

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Write a polynomial function of least degree with integral coefficients that has the given zeros.

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Find all roots.

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Find all roots.

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Find all zeros of g(x) = x^4 - 5x^2 + 4.

• x = -4, -2 , 1, 2

• x = -2, -1 , 1, 2

• x = -1, 0 , 1, 4

• x = -1, 1 , 2, 4

Solve x⁴ - 256 = 0

• x = 4, x = - 4

• x = 4, x = 4i

• x = 4, x -4, x = 4i

• x = 4, x -4, x = 4i,         x = -4i

Find the zeros of the polynomial.

• A

• B

• C

• D

• Zero of the polynomial

• zero coefficient

• rational number

• Can't decide

Answer explanation

The roots of the polynomial equation can be found by factoring the equation as (x-1)(x+2)(x-3)=0. Therefore, x = 1, -2, 3.

If a polynomial has 2 factors, it will have 2 zeros (or 1 zero with a multiplicity of 2).

• True

• False