Complex Numbers And Quadratic Equations question 178
Question: If $ \sin \alpha ,\cos \alpha $ are the roots of the equation $ ax^{2}+bx+c=0 $ , then [MP PET 1993]
Options:
A) $ a^{2}-b^{2}+2ac=0 $
B) $ {{(a-c)}^{2}}=b^{2}+c^{2} $
C) $ a^{2}+b^{2}-2ac=0 $
D) $ a^{2}+b^{2}+2ac=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
As given, $ \sin \alpha +\cos \alpha =-\frac{b}{a}, $ $ \sin \alpha \cos \alpha =\frac{c}{a} $ To eliminate $ \alpha $ , we have $ 1={{\sin }^{2}}\alpha +{{\cos }^{2}}\alpha ={{(\sin \alpha +\cos \alpha )}^{2}}-2\sin \alpha \cos \alpha $ $ =\frac{b^{2}}{a^{2}}-\frac{2c}{a}\Rightarrow a^{2}-b^{2}+2ac=0 $
BETA
