Question

Three roots of f(x)=x^4−2x^3+ax^2+bx+c are −5, −3 and 4. What is the value of a+b+c?

Answer 1

If the other root is k,
f(x) = (x+5)(x+3)(x-4)(x-k)
= x^4 + (4-k)x^3 - (4k+17)x^2 + (17k-60)x + 60k

So,

4-k = -2
k=6

a = -(4k+17) = -41
b = 17k-60 = 42
c = 60*6 = 360

a+b+c = 361

Answer 2

thanks STEVE...