if both (x-1) and (x+1) are factors of x^3-3ax^2+bx+5 find a and b
Answers
(x-1) and (x+1) are factors of the given polynomial.
x-1 = 0. ; x+1 = 0
x = 1. ; x = -1
Put x= -1,1 to find a and b
First,put x = 1
ax³+x²-2x+b = 0
a(1)³+(1)²-2(1)+b=0
a+1-2+b=0
a+b-1 = 0
a+b = 1 --------(1)
Put x = -1
a(-1)³+(-1)²-2(-1)+b = 0
a(-1)+1+2+b = 0
-a+b+3 = 0
-a+b = -3 -------(2)
(1)+(2)
a+b = 1
-a+b=-3
-----------
2b = -2
b = -2/2
b = -1
Put b= -1 in (1)
a+(-1) = 1
a-1 = 1
a=1+1
a=2
Therefore, a = 2 and b = -1
Hope it helps
Answer:
Step-by-step explanation:
(x-1) and (x+1) are factors of the given polynomial.
x-1 = 0. ; x+1 = 0
x = 1. ; x = -1
Put x= -1,1 to find a and b
First,put x = 1
ax³+x²-2x+b = 0
a(1)³+(1)²-2(1)+b=0
a+1-2+b=0
a+b-1 = 0
a+b = 1 --------(1)
Put x = -1
a(-1)³+(-1)²-2(-1)+b = 0
a(-1)+1+2+b = 0
-a+b+3 = 0
-a+b = -3 -------(2)
(1)+(2)
a+b = 1
-a+b=-3
-----------
2b = -2
b = -2/2
b = -1
Put b= -1 in (1)
a+(-1) = 1
a-1 = 1
a=1+1
a=2
Therefore, a = 2 and b = -1
Hope it helps
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