Complex Numbers And Quadratic Equations question 172
Question: If the roots of the equation $ qx^{2}+px+q=0 $ where p, q are real, be complex, then the roots of the equation $ x^{2}-4qx+p^{2}=0 $ are
Options:
A) Real and unequal
B) Real and equal
C) Imaginary
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The given equations are $ qx^{2}+px+q=0 $ …..(i) and $ x^{2}-4qx+p^{2}=0 $ …..(ii) Roots of (i) are complex, therefore $ p^{2}-4q^{2}<0 $ Now discriminant of (ii) is $ 16q^{2}-4p^{2}=-4(p^{2}-4q^{2})>0 $ Hence, roots are real and unequal.
BETA
