How do you find the polynomial function with leading coefficient 2 that has the given degree and zeroes: degree 3: zeroes 2, 1/2, 3/2?

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Answer 1 · 2016-09-04T09:29:41

The polynomial function is
#2x^3-8x^2+19/2x-3#

A polynomial function with zeros as #a#, #b# and #c# can be written as

#(x-a)(x-b)(x-c)#

However, this will give the leading coefficient as #1#. If leading coefficient is #n#, the polynomial would be #n(x-a)(x-b)(x-c)#.

Hence a polynomial function of degree #3#, zeros #2#, #1/2# and #3/2# and leading coefficient #2# is

#2(x-2)(x-1/2)(x-3/2)#

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

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

= #2x^3-8x^2+19/2x-3#