Question

Find a and b if x^2+x-12 divides x^3+ax^2+bx-84

Answer 1

x^2+x-12 = (x-3)(x+4)According to the given condition,x^2+x-12 = (x-3)(x+4) is a factor of x^3+ax^2+bx-84 = f(x). Hence, f(3) = f(-4) = 0Therefore, 27+9a+3b-84=0  or 3a+b-19=0-64 + 16a-4b-84=0 or 4a-b-37=0 Adding these two equations, we get, 7a - 56 = 0 or a = 8So, b = 19-24 = -5