Given x^3 - 10x^2 + ax + b = 0 and two if its roots are 5 and 2, find a and b.
Let the thrird root be u, then:
Originally Posted by Mr_Green
(x-u)(x-5)(x-2) = x^3 - x^2 (u + 7) + x (7u + 10) - 10u
but this is equal to x^3 - 10x^2 + ax + b, so equating the coefficients of
x^2, we see that u=3.
x^3 - 10 x^2 +31 x - 30 = x^3 - 10x^2 + ax + b
so b=30, and a=31.