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prashant prakash

· started a discussion

· 1 Months ago

wrong explanation (Question: 111081.0 )

c/a=1/4

Question:
If \(\alpha\), \(\beta\) are the roots of the quadratic equation 4x2 - 4x +1 = 0, then \(\alpha^3\) + \(\beta^3\) is equal to :
Options:
A) \(\cfrac{1}{4}\)
B) \(\cfrac{1}{8}\)
C) 16
D) 32
Solution:
Ans: (a)

Given equation is 4x2 -4x+ 1 = 0

\(\alpha+\beta=\cfrac{4}{4}=1\)

\(\alpha\beta=\cfrac{1}{4}\)


\(\therefore\) \(\alpha^3+\beta^3= (\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)\)

= \(1^3-\cfrac{3}{4}=\cfrac{1}{4}\)

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