Question
Question: If p,qĪ {1, 2, 3, 4, 5} then number of equations of form p<sup>2</sup>x<sup>2</sup> + q<sup>2</sup>x...
If p,qĪ {1, 2, 3, 4, 5} then number of equations of form p2x2 + q2x + 1 = 0 having real roots is
A
15
B
13
C
16
D
17
Answer
16
Explanation
Solution
Q D = q4 – 4p2 ³ 0
= (q2 + 2p) (q2 – 2p) ³ 0
Ž q2 ³ 2p
If p = 1 then q = 2, 3, 4, 5
p = 2 then q = 2, 3, 4, 5
p = 3 then q = 3, 4, 5
p = 4 then q = 3, 4, 5
p = 5 then q = 4, 5
total possibilities = 16