Complex Numbers And Quadratic Equations question 542
Question: The quadratic equation with real coefficients whose one root is $ 7+5i $ , will be [RPET 1992]
Options:
A) $ x^{2}-14x+74=0 $
B) $ x^{2}+14x+74=0 $
C) $ x^{2}-14x-74=0 $
D) $ x^{2}+14x-74=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ \alpha =7+5i $ , then its conjugate $ \beta =7-5i $ , so required equation is given by $ x^{2}-(\alpha +\beta )x+\alpha \beta =0 $
Þ $ x^{2}-(14)x+(49+25)=0 $
Þ $ x^{2}-14x+74=0 $
BETA
