if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have?

Question

A-2 real, rational roots
B-2 real, irrational roots
C-1 real, irrational roots
D-2 imaginary roots

Answer 1

Hints: here are the possible situations:

When discriminant is negative:
2 imaginary roots

When discriminant is a positive perfect square, such as 1, 4, 9, 16... and all coefficients are rational:
2 real, rational roots

When discriminant is zero, and either coefficient a or b is irrational:
1 real, irrational roots

When discriminant is a positive number but not a perfect square:
2 real, irrational roots