What is the product of the roots of the equation #-2x^2+3x+8=0#?

1 Answer
Dec 17, 2016

Answer:

-4

Explanation:

for any quadratic

#ax^2+bx+c=0" "#if the roots are #" "alpha" "&" "beta#

the sum of roots#" "alpha+beta=-b/a#

the product of the roots#" "alphabeta=c/a#

these results do need to be memorised.

**see proof below.

for #-2x^2+3x+8=0#

product of roots#" "aplhabeta=8/-2=-4#


*proof of results

#ax^2+bx+c=0" "#if the roots are #" "alpha" "&" "beta#

#(x-alpha)(x-beta)=0#

expanding

#x^2-betax-alphax+alphabeta=0#

#x^2color(red)(-(alpha+beta))x+color(blue)(alphabeta)=0" "---(1)#

#ax^2+bx+c=0" "#

#-:a#

#=>x^2+color(red)((b/a))x+color(blue)(c/a)=0" "---(2)#

comparing #""--(1)" "&""--(2)" "#the results follow.