Question

if (x-6) is a factor of x^3+ax^2+bx-b and a-b=7 find the value of a and b

Answer 1

Given that x - 6 is a factor of f(x). SO, substitute x =6 in the given polynomial equation

x^3+ax^2+bx-b = 0

put x = 6

6^3 + a (6^2) + 6b - b =0

216 + 36 a + 5b = 0

SO, 36 a + 5b = -216

also, given a - b = 7

so, 5a - 5b = 35


add these both equations

5b is cancelled

41 a = -181



so, a = -181/41 and b = -468/41

Answer 2

Answer:

a = -181/41 and b = -468/41

Step-by-step explanation:

Given that x - 6 is a factor of f(x). SO, substitute x =6 in the given polynomial equation

x^3+ax^2+bx-b = 0

put x = 6

6^3 + a (6^2) + 6b - b =0

216 + 36 a + 5b = 0

SO, 36 a + 5b = -216

also, given a - b = 7

so, 5a - 5b = 35

add these both equations

5b is cancelled

41 a = -181

so, a = -181/41 and b = -468/41