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Jayant Singh

· started a discussion

· 1 Months ago

good question (Question: 113158.0 )

good question

Question:

If \(\alpha\) and \(\beta\) are the roots of the equation x2 + px + q = 0 then the equation whose roots are \(\alpha\)2 + \(\alpha\)\(\beta\) and \(\beta\)2 + \(\alpha\)\(\beta\) is:

Options:
A) x2 + p2x + p2q = 0
B) x2 - q2x + p2q = 0
C) x2 + q2x + p2q = 0
D) x2 - p2x + p2q = 0
Solution:
Ans: (d) 

\(\alpha\) and \(\beta\) are roots of the equation 

x2 + px + q = 0 

\(\therefore\)  \(\alpha\) + \(\beta\) = -p ...........(i)

and   \(\alpha\)\(\beta\) = q

Now to find the equation whose roots are \(\alpha\)2 + \(\alpha\)\(\beta\) and \(\beta\)2 + \(\alpha\)\(\beta\) 

sum of roots         = \(\alpha\)2 + \(\alpha\)\(\beta\) + \(\beta\)2 + \(\alpha\)\(\beta\) 

= (\(\alpha\) + \(\beta\))2 = p2 

Product of roots    = (\(\alpha\)2 +\(\alpha\)\(\beta\)) (\(\beta\)2 + \(\alpha\)\(\beta\))

= \(\alpha\)\(\beta\) (\(\alpha\) + \(\beta\))2 = qp2

Required equation will be

x2 - (sum of roots) x + products of roots = 0 

or   \(x^2 - p^2 x + p^2q = 0\)

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
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Ashwani Kumar

· commented

· 1 Months ago

great question
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