Complex Numbers And Quadratic Equations question 765
If the roots of the equation $ ax^{2}+x+b=0 $ are real, then the roots of the equation $ x^{2}-4\sqrt{ab}x+1=0 $ will be
Options:
A) Rational
B) Rational
C) Real
D) Imaginary
Show Answer
Answer:
Correct Answer: D
Solution:
$ ax^{2}+x+b=0 $ has real roots Þ $ {{(1)}^{2}}-4ab\ge 0\Rightarrow -4ab\ge -1 $ or $ 4ab\le 1 $ …..(i) Now second equation is $ x^{2}-4\sqrt{ab}x+1=0 $ Therefore $ D=16ab-4, $ from (i) $ D\le 0 $ Hence roots are imaginary.
BETA
