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What is the type of roots of a quadratic equation whose discriminant is greater than zero?

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Real and distinct

Real and Equal

No real roots exist

None of the above

answer is A.

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Detailed Solution

Given the roots of a quadratic equation.
Nature of the roots: - Case 1: - when

D > 0

i.e. b

2 − 4 a c > 0

In this case, the roots are real and distinct.
Case 2: - when

D = 0

i.e. b

2 − 4 a c = 0

In this case, the roots are real and equal.
Case 3: - when

D < 0

i.e b

2 − 4 a c < 0

In this case the roots are not real.
We know the nature of the roots of a quadratic equation. We have two cases of the nature of the roots when the discriminant greater than and equal to zero and roots are real. When

D = 0

, the roots are real and equal. When D

> 0

, the roots are real and distinct.
Therefore, the correct option is 1.

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