Assuming the coefficients are real, the discriminant is non-negative. The reason for this is that in this case, if the solutions are complex, they must needs be conjugats of one another, i.e., two different solutions.
A quadratic equation has one discriminant.
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac
The discriminant
Rational.
If the discriminant of a quadratic equation is zero then it has two identical roots.
A quadratic equation has one discriminant.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
It can tell you three things about the quadratic equation:- 1. That the equation has 2 equal roots when the discriminant is equal to zero. 2. That the equation has 2 distinctive roots when the discriminant is greater than zero. £. That the equation has no real roots when the discriminant is less than zero.
The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac
The discriminant
Rational.
The quadratic has no real solutions.
If the discriminant of a quadratic equation is less than zero then it has no solutions.
Because the square root of the discriminant is a component of the roots of the equation.
The discriminant of the quadratic polynomial ax2 + bx + c is b2 - 4ac.