Question

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

Answer 1

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`

Answer 2

`=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]

Answer 3

`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.