Complex Numbers And Quadratic Equations question 632
Question: A value of b for which the equations $ x^{2}+bx-1=0 $ $ x^{2}+x+b=0 $ have one root in common is
Options:
A) $ -\sqrt{2} $
B) $ -i\sqrt{3} $
C) $ i\sqrt{5} $
D) $ \sqrt{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ \alpha $ be the common root of given equations, then $ {{\alpha }^{2}}+b\alpha -1=0 $ …(1) and $ {{\alpha }^{2}}+\alpha +b=0 $ …(2) Subtracting (2) from (1), we get $ (b-1)\alpha -(b+1)=0 $ or $ \alpha =\frac{b+1}{b-1} $ Substituting this value of a in equation (1), we get $ {{( \frac{b+1}{b-1} )}^{2}}+b( \frac{b+1}{b-1} )-1=0 $ or $ b^{3}+3b=0\Rightarrow b=0, $ $ i\sqrt{3},-i\sqrt{3} $
BETA
