Complex Numbers And Quadratic Equations question 791
Question: Let $ p,q\in {1,2,3,4} $ . The number of equations of the form $ px^{2}+qx+1=0 $ having real roots is [IIT Screening 1994]
Options:
A) 15
B) 9
C) 7
D) 8
Show Answer
Answer:
Correct Answer: C
Solution:
For real roots, discriminant $ \ge 0 $
$ \Rightarrow q^{2}-4p\ge 0\Rightarrow q^{2}\ge 4p $ For $ p=1,q^{2}\ge 4\Rightarrow q=2,3,4 $ $ p=2,q^{2}\ge 8\Rightarrow q=3,4 $ $ p=3,q^{2}\ge 12\Rightarrow q=4 $ $ p=4,q^{2}\ge 16\Rightarrow q=4 $ Total seven solutions are possible.
BETA
