Question

PLEASE HELP ASAP

Which equations have no real solution but have two complex solutions?

3x^2-5x=-8 2x^2=6x-5 12x=9x^2+4 -x^2-10x=34

Answer 1

First option:
`3x^2-5x=-8`

Second option:
`2x^2=6x-5`

Fourth option:
`-x^2-10x=34`

Explanation:

Rewrite each equation in the form
`ax^2+bx+c=0` and then use the Discriminant formula for each equation. This is:

`D=b^2-4ac`

1) For
`3x^2-5x=-8`:

`3x^2-5x+8=0`

Then:

`D=(-5)^2-4(3)(8)=-71`

Since
`D<0` this equation has no real solutions, but has two complex solutions.

2) For
`2x^2=6x-5`:

`2x^2-6x+5=0`

Then:

`D=(-6)^2-4(2)(5)=-4`

Since
`D<0` this equation has no real solutions, but has two complex solutions.

3) For
`12x=9x^2+4`:

`9x^2-12x+4=0`

Then:

`D=(-12)^2-4(9)(4)=0`

Since
`D=0` this equation has one real solution.

4) For
`-x^2-10x=34`:

`-x^2-10x-34=0`

Then:

`D=(-10)^2-4(-1)(-34)=-36`

Since
`D<0`, this equation has no real solutions, but has two complex solutions.