Multiple choice

If both $p$ and $q$ belongs to the set $(1,2,3,4)$, then how many equations of the form $px^2+qx+1=0$ will have real roots ?

  1. $12$
  2. $10$ 
  3. $7$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For real roots, the discriminant D = q^2 - 4p >= 0, so q^2 >= 4p. Given p, q in {1,2,3,4}: If p=1, q^2 >= 4 (q=2,3,4 -> 3 cases). If p=2, q^2 >= 8 (q=3,4 -> 2 cases). If p=3, q^2 >= 12 (q=4 -> 1 case). If p=4, q^2 >= 16 (q=4 -> 1 case). Total = 3+2+1+1 = 7.

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