Question

if (x+1)(x-2) are factors of x^3+ mx^2+2x+n, find the value of m. and n
​

Answer 1

Answer:

m=(-5) and n=(8)

Step-by-step explanation:

Let, P(x)=x³+mx²+2x+n

∴P(-1)=0

∴(-1)³+m(-1)²+2(-1)+n=0

∴-1+m-2+n=0

∴m+n=3             ········     (1)

Also, P(2)=0

∴(2)³+m(2)²+2(2)+n=0

∴8+4m+4+n=0

∴4m+n=-12         ········    (2)

By solving Equation (1) and  (2)

We get, m=(-5)

              n=(8)