Answer:
The discriminant of a quadratic equation is the expression found under the square root sign in the quadratic formula, which is b^2 - 4ac. The discriminant reveals information about the nature of the roots of the equation.
If the discriminant is positive, the quadratic equation has two distinct real roots. This means that the equation can be factored into two linear factors, each of which can be set equal to zero to solve for the roots.
If the discriminant is zero, the quadratic equation has one real root, which is a repeated root. This means that the equation can be factored into a linear factor that occurs twice.
If the discriminant is negative, the quadratic equation has two complex (non-real) roots, which are conjugates of each other. This means that the equation cannot be factored into two linear factors with real coefficients.
In summary, the nature of roots of a quadratic equation is determined by the value of the discriminant, which depends on the coefficients of the quadratic equation.
Explanation: