If a,b, C, d are the roots of x ^ 3 + p * x ^ 2 + qx + r = 0 ; find the equation whose roots are (i) ab, bc , ca (ii) a ^ 2, b ^ 2 , c ^ 2
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Answer:
Let the roots of the equation be a,b,c
a+b+c=p
ab+bc+ca=q
abc=r
1. )∑
a
2
1
=
a
2
b
2
c
2
∑a
2
b
2
=
a
2
b
2
c
2
(a+b+c)
2
−2abc(a+b+c)
=
r
2
p
2
−2pr
2. )∑
a
2
b
2
1
=
a
2
b
2
c
2
(a+b+c)
2
−2(ab+bc+ac)
=
r
2
p
2
−2q
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