Answer:
2x^2 = 6x - 5.
-x^2 - 10x = 34.
These have only complex roots/
Explanation:
3x^2 - 5x = -8
3x^2 - 5x + 8 = 0
There are complex roots if the discriminant 9b^2 - 4ac) is negative.
Here the discriminant D = (-5)^2 - 4*-5*8 = 25 + 160
This is positive so the roots are real.
2x^2 = 6x - 5
2x^2 - 6x + 5 = 0
D = (-6)^2 - 4*2*5 = 36 - 40 = -4
So this has no real roots only complex ones.
12x = 9x^2 + 4
9x^2 - 12x + 4 = 0
D = (-12)^2 - 4*9 * 4 = 144 - 144 = 0.
- Real roots.
-x^2 - 10x = 34
x^2 + 10x + 34 = 0
D = (10)^2 - 4*1*34 = 100 - 136 = -36.
No real roots = only complex roots.