Complex Numbers And Quadratic Equations question 464
Question: If a, b, c, d $ \in $ R, then the equation $ (x^{2}+ax-3b) $ $ (x^{2}-cx+b) $ $ (x^{2}-dx+2b) $ =0 has
Options:
A) 6 real roots
B) at least 2 real roots
C) 4 real toots
D) 3 real roots
Show Answer
Answer:
Correct Answer: B
Solution:
[b] The discriminants of the given equations are $ D_1=a^{2}+12b $ , $ D_2=c^{2}-4b $ and $ D_3=d^{2}-8b $ .
$ \therefore D_1+D_2+D_3=a^{2}+c^{2}+d^{2}\ge 0 $ Hence, at least one $ D_1 $ , $ D_2 $ , $ D_3 $ is non-negative. Therefore, the equation has at least two real roots.
BETA
