How do you form a polynomial function whose zeros, multiplicities and degrees are given: Zeros: -2, 2, 3; degree 3?

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Answer 1 · 2016-11-15T10:58:39

Polynomial function is #x^3-3x^2-4x+12#

A polynomial function whose zeros are #alpha#, #beta#, #gamma# and #delta# and multiplicities are #p#, #q#, #r# and #s# respectively is

#(x-alpha)^p(x-beta)^q(x-gamma)^r(x-delta)^s#

It is apparent that the highest degree of such a polynomial would be #p+q+r+s#.

As zeros are #-2#, #2# and #3# and degree is #3#, it is obvious that multiplicity of each zero is just #1#.

Hence polynomial is #(x-(-2))(x-2)(x-3)#

= #(x+2)(x-2)(x-3)#

= #(x^2-4)(x-3)#

= #x^3-3x^2-4x+12#