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Grade 11Physical Chemistry

If the roots of the equation x^2+px+q=0 differ from the roots of the equation x^2+qx+p=0 by the same quantity then (p is not equal to q) A.p+q+1=0B.p+q+2=0C.p+q+4=0D.none of these

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8 Years agoGrade 11
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ApprovedApproved Tutor Answer8 Years ago
Dear student
 
Let a and b be the roots for first quadratic and c and be the roots for second.
if the root of the equation x²+px+q=0 differ from roots of equation x²+qx+p=0
then,
a – b = c – d = k
Now difference of the roots in terms of sum of roots and prodduct of roots is:
=> |a-b| = root((a+b)^2 – 4ab))
and similarly,
|c-d| = root((c+d)^2 – 4cd))
putting the values we get,
root((-p)^2 – 4q)) – root((-q)^2 – 4p)) = k
Now k could be any assume it be zero
then,
root((-p)^2 – 4q)) – root((-q)^2 – 4p)) = 0
solving we get,
p + q + 4 = 0

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