if x minus 6 is a factor of x cube + ax square + b x minus b and a minus b is equal to 7 then find the value of a and b
Answers
Answer:
a = -181/41
b = -468/41
Step-by-step explanation:
if x minus 6 is a factor of x cube + ax square + b x minus b and a minus b is equal to 7 then find the value of a and b
x-6 is factor of x³ + ax² + bx - b
x - 6 is factor so x = 6 is a zero of polynomial
=> 6³ + a6² +b6 - b = 0
=> 216 + 36a + 6b - b = 0
=> 36a + 5b = -216 - Eq 1
a - b = 7
multiplying by 5
5a - 5b = 35
Adding both equations
36a + 5a = -216 + 35
=> 41a = -181
=> a = -181/41
a - b = 7
=> b = a - 7
=> b = -181/41 - 7
=> b = (-181 - 287)/41
=> b = -468/41
Answer:
a= -181/41, b = -468/41
Step-by-step explanation:
We take note of the equation given in the problem:
1) x^3 +ax^2 +bx-b
2) x-6
3) a-b=7
We find the zeroes of our equation 2, so it will not become x= 6.
Next, we equate our first equation by zero and substitute the value of x.
6^3 +a(6)^2 +b(6) -b =0
216 +36a +6b-b=0
36a+5b = -216
We find the value of a by deriving equation 3
a=b+7
Using the value of a, substitute it in our equation 36a +5b = -216
36(b+7) +5b= -216
36b + 252 +5b = -216
41b/41 = -468/41
b = -468/41
a= -468/41 + 7
a= -181/41