Question

Roots of a quadratic equation can be

• A. equal
• B. real
• C. imaginary
• D. irrational

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A equal
B real
C imaginary
D irrational

Nature of roots

When the co-efficients of a quadratic equation are real, then the nature of the roots is as follows :

Complex roots: If $D<0$, then the roots are complex of the form $A\pm iB.$

Real Roots: If $D>0$, then the roots are real and distinct.

For the particular case, when $D=0$ the roots are real and equal.<br>

Rational and irrational roots

If a, b, c $\in Q$, then

If $D>0$ and a perfect square, then roots are rational.

If $D>0$ and not a perfect square, then roots are irrational.

Hence, all the options are correct.