Question #492ce

1 Answer
MattyMatty
Dec 21, 2017

#"See explanation"#

Explanation:

#"Use the rational roots theorem first."#
#"Search for rational roots of the shape "pmp/q" with p divisor of 2 and q divisor of 16."#
#"You can find "-1/4" and "2" as rational roots."#
#"So (4x+1) and (x-2) are factors."#
#"So divide them away to obtain the third factor :"#
#16x^3-24x^2-15x-2 = (4x+1)^2(x-2).#
#"So we have two times the zero -1/4, so we say that the"#
#"multiplicity of -1/4 is 2."#
#"Note that only x=2 can be solution to the original problem as"#
#"we cannot take the logarithm of negative numbers."#

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