Complex Numbers And Quadratic Equations question 575
Question: If $ \alpha ,\beta $ are the roots of $ x^{2}-2x+4=0 $ , then $ {{\alpha }^{5}}+{{\beta }^{5}} $ is equal to [EAMCET 1990]
Options:
16
32
64
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Here $ {{\alpha }^{2}}+{{\beta }^{2}}=-4,{{\alpha }^{3}}+{{\beta }^{3}}=-16 $ \ $ ({{\alpha }^{2}}+{{\beta }^{2}})({{\alpha }^{3}}+{{\beta }^{3}})={{\alpha }^{5}}+{{\beta }^{5}}+{{\alpha }^{2}}{{\beta }^{2}}(\alpha +\beta ) $
Þ $ (-4)(-16)={{\alpha }^{5}}+{{\beta }^{5}}+(16)(2) $
Þ $ {{\alpha }^{5}}+{{\beta }^{5}}=32 $
BETA
