In a quadratic y = ax² + bx + c, the roots are where y = 0, and the parabola crosses the x-axis. The average of these two roots is the x coordinate of the vertex of the parabola.
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Quadratics can two, one or no real roots.
Then x will have two different distinct roots
If the discriminant of a quadratic equation is 0 then it has two equal real roots.
If the discriminant is negative, the roots will be two unreal complex conjugates. If the discriminate is positive the roots will be real.
If the discriminant of a quadratic equal is zero then it will have two equal roots.