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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

  1. $10$
  2. $7$
  3. $6$
  4. $12$
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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
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