A is a single digit prime no. and B is a natural no. How many equations of the form x^2-4 sqrt(A)*x+ 3B=0 will have real roots?

• For real roots, discriminant>=0
  D>=0 i.e. 16A-12B>=0 i.e. 4A>=3B
  Now, in each case consider A=2,3,5 and 7 (single digit prime no.)
  4*2>=3(1,2)
  4*3>=3(1,2,3,4)
  4*5>=3(1,2,3,4,5,6)
  4*7>=3(1,2,3,4,5,6,7,8,9)
  Thus, we get in all 21 equations which is the required answer
• 10 years agoHelpfull: Yes(1) No(0)