Δ = b^2-4ac Calculate with a plus or minus sign.

Δ is the discriminant of a quadratic equation, Δ=b^2-4ac after reducing the quadratic equation to its general form, i.e., ax^2+bx+c=0.

Derivation process: the formula for finding the roots of a quadratic equation is: (-b±b^2-4ac under the root sign) divided by 2a.

If there are real roots of the quadratic equation, the inner equation under the root sign should be greater than zero. the equation under the root sign has to be greater than zero. That's why b^2-4ac is called the discriminant, and the magnitude in relation to zero determines whether the equation has any real roots.

Extension:

Algebraically, Δ is used as a discriminant to represent the roots of an equation.

Discriminant of a quadratic equation: Δ=b?-4ac

1) when Δ>0, the equation has two unequal real roots;

2) when Δ=0, the equation has two equal real roots;

3) when Δ<0, the equation has no real roots but has 2 ****-conjugate complex roots.

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