find the values of m and n so that x+1 and x-1 are factors of x^3-6x^2+mx-n
Please answer with steps
Answers
Answer:
m = 11
n = 6
Step-by-step explanation:
Given,
(x-1) & (x-2) are the factors of f (x).
By using factor theorem,
So we can substitute the the value of x as x = 1 or x = 2.
• firstly x = 1
x^3 - 6x^2 + mx - n = 0
=> (1)^3 - 6(1)^2 + m(1) - n = 0
=> 1 - 6 + m - n = 0
=> m - n = 5 ...(1)
• Now x = 2
x^3 - 6x^2 + mx - n = 0
=> (2)^3 - 6(2)^2 + m(2) - n = 0
=> 8 - 24 + 2m - n = 0
=> 2m - n = 16 ... (2)
By subtracting equation (1) from (2) we get
=> 2m - n - m + n = 16 - 5
=> m = 11.
From equation (1), we get,
11 - n = 5
=> n = 11 - 5 = 6
Hence,
m = 11
n = 6
value of m & n are 11 & 6 respectively.
Answer:
The values of m and n are-1 and -6
Step by step explanation:
→Factors of the polynomial x+1 and x-1
x+1=0,x-1=0
x=-1 ,x=1
Therefore x=±1
→The value of m and n [when x=1]
→x³-6x²+mx-n=0
→1³-6×1²+m×1-n=0
→1-6+m-n=0
→-5+m-n=0
→m-n=5 —first equation
→x³-6x²+mx-n=0
→-1³-6×[-1]²+m×[-1]-n=0
→-1-6×1-m-n=0
→-7-m-n=0
→-m-n=7— as second equation
first equation+second equation
→ m-n=5
→ -m-n=7
→ 2m=-2
→ m=-1
The value of n is
→m-n=5
→-1-n=5
→-n=6
→n=-6