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Answers
Answer:
a = 3, b = -3
Step-by-step explanation:
If (x + 1) is a solution:
x + 1 = 0
x = -1
The equation is 0 when x = -1:
(-1)⁴ + a(-1)³ + 2(-1)² - 3(-1) + b = 0
1 - a + 2 + 3 + b = 0
6 - a + b = 0
a = b + 6
if (x - 1) is a solution:
x - 1 = 0
x = 1
The equation is 0 when x = 1:
(1)⁴ + a(1)³ + 2(1)² - 3(1) + b = 0
1 + a + 2 - 3 + b = 0
a + b = 0
Putting the two equation together:
a = b + 6 -------- [ 1 ]
a + b = 0 -------- [ 2 ]
Sub [ 1 ] into [ 2 ]:
(b + 6) + b = 0
2b + 6 = 0
2b = -6
b = -3
Sub b = -3 into [ 1 ] :
a = b + 6
a = -3 + 6
a = 3
Answer: a = 3, b = -3
hey there,
In this question, they are saying that (x+1) , (x-1) are the factors so,
x+1=0
x= -1
And
x-1=0
x= 1
solving by keeping x= -1 in the equation
(-1)^4+a(-1)^3+2*(-1)^2-3*(-1)+b =0
1-a+2+3+b =0
6-a+b =0
-a+b= -6
a-b= 6 .............(1)
solving by keeping x=1 in the equation
(1)^4+a*(1)^3+2*(1)^2-3*(1)+b =0
1+a+2-3+b =0
a+b =0 ................(2)
solving (1) and (2) we get,
2a =6
a=3
keeping a=3 in equation (2) we get,
3+b=0
b= -3
hope you understand it
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...........................TNX........................