The discriminant of a quadratic equation is given by b^2 - 4ac where b is the constant in front of the x term, a is the constant in front of the x^2 term and c is the constant at the end.
A negative discriminant means b^2 - 4ac < 0
An example would be 2x^2 -3x + 3 = 0
The discriminant = (-3)^2 - 4(2)(3) = 9 - 24 = -15
But we can still solve this Felix, if we use the Quadratic formula and imaginary numbers.
Remember the quadratic formula Felix? That's -b +/-square root of the discriminant / 2a
So then, x = -(-3) +/- sqrt(-15) / 2(2) = 3 +/- sqrt(-15) / 4
Now Felix, I know you're think we can't take the square root of a negative number. But we can if we us i instead of -1 inside the radical.
So then, x = 3 +/- i sqrt(15) / 4 = 3/4 +/- i sqrt(15)/4
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