Question

what is the value of the discriminant of the quadratic equation -1=5x^2 -2x and what does its values mean?

Answer 1

If you write in standard form for a quadratic: ax^2+bx+c. The discriminant is b^2-4ac, so given -1=5x^2-2x, or 5x^2-2x+1=0, the discriminant is 4-4(5)(1)=-16. The discriminant is used to give information about the roots (a.k.a. zero or solution) of a quadratic. If it's positive, it means that the quadratic has 2 real roots. If it's 0, it has a double root. And, if it's negative, like in this question, it has no real roots.

EXTRA
If you want to know where the discriminant comes from, it is derived from the quadratic formula, which is a more straightforward method of finding roots.

Answer 2

The discriminant of any quadratic equation y=ax^2+bx+c is b^2-4ac.
Move -1 over to the other side, making it equal to zero.
5x^2-2x+1=0
Now plug in.
(-2)^2-4*5*1=-16.
The discriminant is -16. The discriminant of any quadratic equation could have 3 meanings.
Assume d is discriminant.
d<0 means there are no REAL solutions to the equation.
d>0 means there are 2 distinct real solutions.
d=0 means there is one real repeated solution.
In this case, the answer is:
discriminant: -16
There are no real solutions to this quadratic equation. (there could be complex roots though.)