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Given=x³+2x²+ax+b=f(x)
1st factor=x+1
x=-1
f(-1)=-1+2-a+b
=-a+b+1 (1)
2nd factor=x-1
x=1
f(1)=a+b+3 (2)
Solving (1) and (2), we get,
∴a=-1 and b=-2
1st factor=x+1
x=-1
f(-1)=-1+2-a+b
=-a+b+1 (1)
2nd factor=x-1
x=1
f(1)=a+b+3 (2)
Solving (1) and (2), we get,
∴a=-1 and b=-2
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x³ +2x² + ax + b is a polynomial equation . which two factors are ( x -1) and ( x +1)
it means it's two roots are 1 , -1
so,
put x = 1
(1)³ +2(1)² +a(1) + b =0
a + b = -3 ------------(1)
put x = -1
(-1)³ +2(-1)² +a(-1) + b =0
b - a +1 =0
a - b = 1 ------(2)
solve equations (1) and (2)
a = -1 and b = -2
it means it's two roots are 1 , -1
so,
put x = 1
(1)³ +2(1)² +a(1) + b =0
a + b = -3 ------------(1)
put x = -1
(-1)³ +2(-1)² +a(-1) + b =0
b - a +1 =0
a - b = 1 ------(2)
solve equations (1) and (2)
a = -1 and b = -2
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