Question #fa294

1 Answer
Jim G.
Nov 29, 2017

#x=-3/2,x=2" (multiplicity 2)"#

Explanation:

#"note that for x = 2"#

#f(2)=16-20-8+12=0#

#rArr(x-2)" is a factor of "f(x)#

#color(red)(2x^2)(x-2)color(magenta)(+4x^2)-5x^2-4x+12#

#=color(red)(2x^2)(x-2)color(red)(-x)(x-2)color(magenta)(-2x)-4x+12#

#=color(red)(2x^2)(x-2)color(red)(-x)(x-2)color(red)(-6)(x-2)cancel(color(magenta)(-12))cancel(+12)#

#rArrf(x)=(x-2)(2x^2-x-6)#

#color(white)(rArrf(x))=(x-2)(x-2)(2x+3)#

#rArr(x-2)^2(2x+3)=0#

#rArrx=2" (multiplicity 2) and "x=-3/2#

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