Math, asked by littlebittleeditz, 1 day ago

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​

Answers

Answered by kumarrk1562
1

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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