Question

Select the two values of x that are roots of this equation 2x²-11x+15=0

Answer 1

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

Explanation:

`\mathrm{Factor\:}2x^2-11x+15`

`\mathrm{Break\:the\:expression\:into\:groups}`

`\left(2x^2-5x\right)+\left(-6x+15\right)`

`\mathrm{Factor\:out}\:x\:\mathrm{from}\:2x^2-5x:\quad \:x\left(2x-5\right)`
`\mathrm{Factor\:out}\:-3\:\mathrm{from}\:-6x+15:\quad \:-3\left(2x-5\right)`

`x\left(2x-5\right)-3\left(2x-5\right)`

`\mathrm{Factor\:out\:common\:term\:}2x-5`

`\left(2x-5\right)\left(x-3\right)`

`\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0`

`2x-5=0\quad \mathrm{or}\quad \:x-3=0`

`\mathrm{Solve\:}\:2x-5=0:\quad x=(5)/(2)`

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

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

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