Question

If a,b,c are the roots of x^3-2x^2+x-3=0, find the value of

(b+c)(c+a)(a+b)

Answer 1

You might recall that for any quadratic of the form

ax^2 + bx + c = 0 , if the roots are r1 and r2
then r1+r2 = -b/a and r1r2 = c/a

A similar relation exists for a cubic of the form
ax^3 + bx^2 + cx + d = 0 , with roots r1, r2, and r3
r1 + r2 + r3 = -b/a
r1r2r3 = -d/a
and also
r1r2 + r1r3 + r2r3 = c/a

so in your case
a+b+c = 2
abc = 3
ab + ac + bc = 1

then (b+c)(c+a)(a+b)
= (b+c)(ac + bc + a^2 + ab)
= abc + b^2c + a^2b + ab^2 + ac^2 + bc^2 + a^2c + abc
= .....

see if you can anywhere from here.