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Asked by  | 18th 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.

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Answered by  | 18th Feb, 2010, 02:29: PM

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