Discriminant and Number of Roots

Discriminant and Number of Roots

For a quadratic equation written as (ax^2+bx+c=0), the discriminant is [ \Delta=b^2-4ac. ] It tells you how many real roots the equation has.

1) Identify (a), (b), and (c)

Make sure the equation is in standard form. Then read off the coefficients carefully, including signs.

2) Compute the discriminant

Substitute the values into (\Delta=b^2-4ac), then simplify step by step.

3) Interpret the result

• If (\Delta>0), there are two distinct real roots.
• If (\Delta=0), there is one real root repeated twice.
• If (\Delta<0), there are no real roots.

4) Check your work

Recalculate the substitution if needed, especially when negative numbers are involved. A sign mistake is the most common error.

Quick strategy

If the task asks only for the number of roots, you usually do not need to solve the equation completely. The discriminant alone is enough.

Final check

Your answer should be simplified and should match the sign of (\Delta): positive, zero, or negative.