Functions

Asked by arvind95 | 26th Jul, 2012, 07:41: PM

Expert Answer:

It is given that p, q, r are roots of the equation f(x) = 0
So, f(p) = f(q) = f(r) = 0
 
Therefore,
ap3 + bp2 + cp + d = 0
aq3 + bq2 + cq + d = 0
ar3 + br2 + cr + d = 0
 
Adding the above three equations, we get,
a(p3 + q3 + r3) + b(p2 + q2 + r2) + c(p + q + r) + d = 0
a(p3 + q3 + r3) + b[(p + q + r)2 - 2(pq + qr + pr)] + c(p + q + r) + d = 0            ... (1)
 
Also, we have:
p + q + r = -b/a
pq + qr + pr = c/a
pqr = -d/a
 
On substituting these values in equation (1), you will get p3 + q3 + r3 in terms of a, b, c and d.

Answered by  | 1st Aug, 2012, 10:13: AM

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