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Because the square root of the discriminant is a component of the roots of the equation.

Q: Why the discriminant of a quadratic is useful in algebra?

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I am assuming that "an algebra equation" refers to a quadratic equation and not a higher polynomial.For a quadratic equation of the form y = ax^2 + bx + c, where a, b and c are real numbers and a is non-zero, the discriminant is b^2 – 4ac.

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

b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).

Related questions

I am assuming that "an algebra equation" refers to a quadratic equation and not a higher polynomial.For a quadratic equation of the form y = ax^2 + bx + c, where a, b and c are real numbers and a is non-zero, the discriminant is b^2 – 4ac.

A quadratic equation has one discriminant.

The form of the quadratic is ax2+bx+c, so the discriminant is b2-4ac.

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.

If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.

The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac

b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).

If the discriminant of a quadratic equation is zero then it has two identical roots.

The discriminant

The discriminant is -32.

The discriminant of the quadratic polynomial ax2 + bx + c is b2 - 4ac.

The discriminant must be a positive number which is not a perfect square.