Question

Which of the following represents the zeros of f(x) = x3 − 12x2 + 47x − 60

Answer 1

f(x) = x • 3 • 2 + 47x - 60
fx =3x - 24x + 47x - 60
fx = 26x - 60
x = - 60/f - 26

Answer 2

Answer:
`x=3,\:x=4,\:x=5`.

Step-by-step explanation: Given polynomial function
`f(x) = x^3-12x^2+47x-60`.

`\mathrm{Use\:the\:rational\:root\:theorem}\\`

`p=60,\:\quad q=1`

`\mathrm{The\:dividers\:of\:}p:\quad 1,\:2,\:3,\:4,\:5,\:6,\:10,\:12,\:15,\:20,\:30,\:60,\:\quad \mathrm{The\:dividers\:of\:}q:\quad 1`

`\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm (1,\:2,\:3,\:4,\:5,\:6,\:10,\:12,\:15,\:20,\:30,\:60)/(1)`

`(3)/(1)\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x-3`

`(x^3-12x^2+47x-60)/(x-3)=x^2-9x+20 \ \  By \ long \ division.`

`\mathrm{Factor}\:x^2-9x+20:\quad \left(x-4\right)\left(x-5\right)`

Therefore,

`x^3-12x^2+47x-60=\left(x-3\right)\left(x-4\right)\left(x-5\right)`

`\mathrm{Solve\:}\:x-3=0:\quad x=3`

`\mathrm{Solve\:}\:x-4=0:\quad x=4`

`\mathrm{Solve\:}\:x-5=0:\quad x=5`

`\mathrm{The\:final\:solutions\:to\:the\:equation\:are:}`

`x=3,\:x=4,\:x=5`