CBSE Class 10 Answered
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Asked by | 18 Feb, 2010, 01:45: PM
Expert Answer
α+β+γ = -3p
αβ + βγ + γα = 3q
αβγ = -r
If the roots are to be in arightmatic progression then,
α = a-d; β = a; γ = a+d
α+β+γ = 3a = -3p
a = -p
and
αβγ = (a2-d2)a = -r
(a2-d2)a = -r ................(1)
Put the value of a = -p
we find,
d = (p2 - r/p)
Also,
αβ + βγ + γα = 3q
a2 - ad + a2 + ad + a2 - d2 = 3q
2a2 + a2 - d2 = 3q
2a2 + a2 - d2 = 3q
d = (3p2 - 3q)
Equating the two d's
(3p2 - 3q) = p2 - r/p
Hence, p, q and r must satisfy this relation if the roots are to be in AP.
Regards,
Team,
TopperLearning.
Answered by | 18 Feb, 2010, 02:29: PM
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