Question

Find the values of m and n in the polynomial 2x³+mx²+nx-14 such that (x-1). and(x+2) are its factor

Answer 1

hope this helps you ☺☺

Answer 2

Answer:

m = 9 and n = 3

Step-by-step explanation:

Given polynomial   P(x) = 2x³ + mx² + nx - 14 _(1)

factors of the given polynomial are (x-1) and (x+2)

here we need to find values of m and n  

given  (x-1)  and  (x+2) are the factors

⇒     x-1 =0                x+2 =0

         x = 1                    x = -2

(x-1) and (x+2) are factors of polynomial (1)

then  P(1) and P(-2) will be equals to zero  

⇒ P(1)  =  2(1)³ + m(1)² + n(1) - 14 = 0

           ⇒  2 + m + n - 14 = 0

           ⇒  m + n - 12 = 0 _ (2)  

⇒ P(-2) =  2(-2)³ + m(-2)² + n(-2) - 14 = 0

            ⇒ 2(-8)  + m(4) - 2n -14 = 0

            ⇒ - 16 + 4m - 2n  - 14 = 0

            ⇒   4m - 2n - 30 = 0

            ⇒   2m - n - 15 = 0 _(3)      [ divided by 2 ]  

add (2) and (3)

            m + n - 12 + 2m - n - 15 = 0

            3m - 27 = 0

            3m = 27

            m = 9

substitute  m = 9 in (2)

            9 + n - 12 =  0

            n - 3 = 0

            n = 3