Question
Thu July 26, 2012 By:
 
Let f(x)=ax^3+bx^2+cx+d, where a,b,c,d are known constants. Let p,q,r be the real roots of the equation f(x)=0.Express p^3+q^3+r^3 in terms of a,b,c&d.

Functions

Expert Reply
Wed August 01, 2012
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.
Mon July 17, 2017

plz.. solve Q10

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