if X + 1 and x minus one of the factor of ax cube +x square - 2 X + B then find the value of a and b
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Let A(x) = axe+x-ray+b
x+1 and x-1 are factors of A(x).
therefore -1 and 1 are zeroes of A(x)
A(-1)= a(-1)³ +(-1)² -2(-1)+b=0
=-a+1+2+b
a=3+b. (eq. I)
A(1) = a(1)³+(1)² -2+b=0
a+1-2+b=0
3+b+1-2+b=0. (from eq. I)
2b+2=0
2b = -2
b= -1
now,
a= 3+b
= 3+(-1)
= 3-1
= 2
therefore a =2. and. b = -1
x+1 and x-1 are factors of A(x).
therefore -1 and 1 are zeroes of A(x)
A(-1)= a(-1)³ +(-1)² -2(-1)+b=0
=-a+1+2+b
a=3+b. (eq. I)
A(1) = a(1)³+(1)² -2+b=0
a+1-2+b=0
3+b+1-2+b=0. (from eq. I)
2b+2=0
2b = -2
b= -1
now,
a= 3+b
= 3+(-1)
= 3-1
= 2
therefore a =2. and. b = -1
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