Question

Find the value of m and n so that x – 1 and x + 2 both are factors of x^3 + (3m + 1) x^2 + nx − 18

Answer 1

Answer:

n = 7

m = 1

Step-by-step explanation:

Let f(x) = x3 + (3m + 1) x2 + nx − 18

x − 1 = 0 ⇒ x = 1

x − 1 is a factor of f(x). So, remainder = 0

--->(the image that is attached )

Adding (1) and (2), we get

9m − 27 = 0

m = 3

Putting the value of m in (1), we get

3(3) + n − 16 =0

9 + n − 16 = 0

n = 7