SOLUTION: Find the discriminant and state the nature of the roots: -6x^2-3x+2=0 and x^2+6x=0 I don't understand what the question is saying.

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Question 147845: Find the discriminant and state the nature of the roots: -6x^2-3x+2=0 and x^2+6x=0
I don't understand what the question is saying.
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant comes from the quadratic formula. It is what is under the root.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
This is for form ax^2+bx+c=f(x)
So, now just determine b^2-4ac given each equation.
9-4(-6)(2)=9+48=57. Because 57>0, we will have 2 real roots due to the quadratic formula's +/-.

Now for the second equation.
36. Because 36>0, we will have 2 real roots due to the quadratic formula's +/-.
I will tell you what happens in all other cases.
If discriminant<0 we will have 2 imaginary roots.
If discriminant=0 we will have 1 real root. These follow because of what happens with the root by definition.