If the discriminant is negative,
then it will have 2 solutions unequal, imaginary numbers
If the discriminant is negative, it means that the quadratic equation has no real roots. In other words, the solutions to the equation are complex numbers. This can be understood by looking at the formula for the quadratic equation:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
The expression under the square root sign is the discriminant, denoted by the symbol ‘Δ’.
If Δ < 0, then the square root of a negative number is involved in the formula, which produces complex roots because we cannot take the square root of a negative number in the real number system. So, if you are given a quadratic equation and the discriminant is negative, you can conclude that the roots of the quadratic equation are complex. This also means that the graph of the quadratic equation does not intersect the x-axis, since there are no real solutions for x where the equation equals zero.
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