+452 Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Compute p^2 qrs + pq^2 rs + pqr^2 s + pqrs^2.
+113 The value of the expression
p2qrs+pq2rs+pqr2s+pqrs2
π2πππ +ππ2ππ +πππ2π +ππππ 2
is
answer is 62!
+130474 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Simplify as
x^4 + 2x^3 + 16x^2 + 20x - 31
Note that
p^2 qrs + pq^2 rs + pqr^2 s + pqrs^2 can be written as
pqrs ( p + q + r + s)
The sum of the roots = -2/1 = -2
The product of the roots -31/1 = -31
So
-31 (-2) = 62
