How do you factor #3x^2-8x+15#?

3 Answers
Nov 19, 2017

if you are looking for real roots as the answer then there are no real roots. If you are looking for imaginary roots as the answers then the roots are #(-8+-10.77i)/6#

Explanation:

the given equation is #3x^2-8x+15# this can be factord using the quadratic formulae i.e., #(-b+-sqrt(b^2-4ac))/(2a)# here #a=3,b=-8,c=+15# substituting in the formula we get #(8+-sqrt(64-180))/6=(8+-sqrt(-116))/6~~(8+-10.77i)/6# #:.# the roots are #(-8+-10.77i)/6#

Nov 19, 2017

#=3(x-1.333+1.795i)(x-1.33-1.795i)#

Explanation:

#3x^2-8x+15 = 3(x^2-8/3x) +15#

#=3{x^2-8/3x +(4/3)^2} -16/3+15#

#=3{(x-4/3)^2 } +29/3#

#=3{(x-1.333)^2 +29/9}#

#=3{(x-1.333)^2 -29/9i^2} ; [i^2=-1]#

#=3{(x-1.333)^2 -(1.795i)^2} [ a^2-b^2=(a+b)(a-b)]#

#=3(x-1.333+1.795i)(x-1.33-1.795i)# [Ans]

Nov 19, 2017

#x=8±sqrt(−116)/6#
Answer:
No real solutions.

Explanation:

If#3x^2-8x+15=0# then:-

Step 1: Use quadratic formula with a=3, b=-8, c=15.
#x=−b±sqrt(b^2−4ac)/(2a)#
#x=−(−8)±sqrt((−8)^2−4(3)(15))/(2(3))#
#x=8±sqrt(−116)/6#
Answer:
No real solutions.