If a,b and c are the roots of x^3+px^2+qx+r, then how can we find the value of sum (b^2+c^2)/(bc)

Gillian Cooper

Gillian Cooper

Answered question

2022-09-22

If a , b and c are the roots of x 3 + p x 2 + q x + r, then how can we find the value of b 2 + c 2 b c

Answer & Explanation

Alec Reid

Alec Reid

Beginner2022-09-23Added 9 answers

I think you are asking for
( 1 ) a 2 + b 2 a b + b 2 + c 2 b c + c 2 + a 2 c a ,
or perhaps twice this quantity. If you bring Expression (1) to a common denominator, you will get
a 2 c + b 2 c + b 2 a + c 2 a + c 2 b + a 2 b a b c .
Note that
( a + b + c ) ( a b + b c + c a ) = a 2 c + b 2 c + b 2 a + c 2 a + c 2 b + a 2 b + 3 a b c .
Thus
a 2 + b 2 a b + b 2 + c 2 b c + c 2 + a 2 c a = ( a + b + c ) ( a b + b c + c a ) 3 a b c a b c .
Everything term on the right-hand side is expressible simply in terms of the coefficients.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?