Question

Which of the following represents the zeros of f(x) = 2x3 − 5x2 − 28x + 15?

Answer 1

I think it is 5, -3, 1/2.

Answer 2

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

`a_0=15,\:\quad a_n=2`

`\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:5,\:15,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2`

`\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm (1,\:3,\:5,\:15)/(1,\:2)`

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

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

`\mathrm{Compute\:}(2x^3-5x^2-28x+15)/(x+3)\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }2x^2-11x+5`

`=\left(x+3\right)\left(2x^2-11x+5\right)`

`Factor: 2x^2-11x+5`

`2x^2-11x+5=\left(2x^2-x\right)+\left(-10x+5\right)`

`=x\left(2x-1\right)-5\left(2x-1\right)`

`2x^3-5x^2-28x+15=\left(x+3\right)\left(x-5\right)\left(2x-1\right)`

`\left(x+3\right)\left(x-5\right)\left(2x-1\right)=0`

`\mathrm{Using\:the\:Zero\:Factor\:Principle:}`

thus zeros of f(x) is

`x=-3,\:x=5,\:x=(1)/(2)`