Complex Numbers And Quadratic Equations question 764
Question: If the roots of the equations $ px^{2}+2qx+r=0 $ and $ qx^{2}-2\sqrt{pr}x+q=0 $ be real, then
Options:
A) $ p=q $
B) $ q^{2}=pr $
C) $ p^{2}=qr $
D) $ r^{2}=pq $
Show Answer
Answer:
Correct Answer: B
Solution:
Equations $ px^{2}+2qx+r=0 $ and $ qx^{2}-2(\sqrt{pr})x+q=0 $ have real roots, then from first $ 4q^{2}-4pr\ge 0 $ Þ $ q^{2}-pr\ge 0\Rightarrow q^{2}\ge pr $ …..(i) and from second $ 4(pr)-4q^{2}\ge 0 $ (for real root ) Þ $ pr\ge q^{2} $ …..(ii) From (i) and (ii), we get result $ q^{2}=pr $ .
BETA
