Question

6.If 2x3 + mx2 + nx - 14 is exactly divisible by x2 + x - 2, then the values of m and n are
respectively
1) 3,9
2) 9,3
3) 3,3
4) 9,9

please answer fast and in full steps! ​

Answer 1

Step-by-step explanation:

check this pictures ☝☝☝☝

Answer 2

Answer:

If 2x3 + mx2 + nx - 14 is exactly divisible by x2 + x - 2, then the values of m and n are 9,3 respectively. Option (2)

Step-by-step explanation:

let f (x) = 2x³ + mx² + nx - 14

Since x-1 is factor substitute x=1 in f(x)

f (1) = 0

2(1)³ + m(1)² + n(1) - 14 = 0

2 + m + n - 14 = 0

m + n = 12......... equation 1

Since x+2 is a factor substitute x=-2 in f(x)

f (-2) = 0

2(-2)³ + m(-2)² + n(-2) - 14 = 0

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

4m - 2n = 30

2m - n = 15........ equation 2

Add equation 1 and equation 2

equation 1 + equation 2:

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

3m = 27

m = 9

substitute m=9 in equation 1:

9 + n = 12

n = 3