CAT 2003 | Question: 2-88

Question

If both $a$ and $b$ belong to the set $\{1, 2, 3, 4\}$, then the number of equations of the form $ax^2 + bx + 1 = 0$ having real roots is

• A. $10$
• B. $7$
• C. $6$
• D. $12$

Answer 1

Given - a and b belong to set {1, 2, 3, 4}.

ax^2+bx+1=0.

To have real roots,

 b^2 >=4.a.

If b = 4, then 'a' can be 1, 2, 3, 4        ( 4 possibilities )

If b = 3, then 'a' can be 1, 2.               ( 2 possibilities )

If b = 2, then 'a' can be 1                    (1 possibility)

If b = 1, then no value of a.                ( 0 possibility)

Ans- B. 7