Arthur D. answered 11/27/17
Tutor
4.9
(125)
Mathematics Tutor With a Master's Degree In Mathematics
3x^2+2x+k=0
use the quadratic formula
(-2±√(4-12k))/6
(-2+√(4-12k))/6 and (-2-√(4-12k))/6 are the roots
2(-2+√(4-12k))/6=(-3)(-2-√(4-12k))/6 because 2x1=-3x2
simplify
(-2+√(4-12k))/3=(2+√(4-12k))/2
cross multiply
-4+2√(4-12k)=6+3√(4-12k)
simplify
-4-6=3√(4-12k)-2√(4-12k)
-10=√(4-12k)
square both sides
100=4-12k
100-4=-12k
96=-12k
k=96/(-12)
k=-8 answer
3x^2+2x-8=0 is the equation
roots are (-2±√100)/6
(-2±10)/6
-12/6 and 8/6
x=-2 and x=4/3
check: 2(-2)=-3(4/3), -4=-4