How do you solve the quadratic using the quadratic formula given #4x^2+11x=3x-10# over the set of complex numbers?

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Answer 1 · 2017-10-24T13:02:20

Solution: #x in { -1+- 1/2sqrt6 i}#

# 4x^2+11x=3x-10 or 4x^2+8x+10=0#

# a=4 ,b=8 ,c=10 ; D= b^2-4ac=64-160 = -96 #

Discriminant is negative , so it has complex roots .

Quadratic formula: #x= (-b+-sqrtD)/(2a)#

#:.x= (-8+-sqrt(-96))/8 # or

#x= (-8+-sqrt96*i^2)/8 = -1 +- (4sqrt6)/8 i# or

#x= -1+- 1/2sqrt6 i# or

#:. x in { -1+- 1/2sqrt6 i}#

Solution: #x in { -1+- 1/2sqrt6 i}# [Ans]