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प्रश्न
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
उत्तर
Let f(x) = x4 + ax3 − 3x2 + 2x + b be the given polynomial.
By factor theorem, (x+1)and (x-1)are the factors of f(x) if f(−1) and f(1) both are equal to zero.
Therefore,
`f(-1) = (-1)^4 + a(-1)^3 -3(-1)^2 +2(-1) + b = 0 ..... (1)`
` 1-a - 3- 2 + b = 0`
`-a + b = 4 .......(1)`
and
`f(1) = (1)^4 + a(1)^3 +2(1) +b = 0`
`1 + a-3 + 2 = 0`
`a+b = 0 .....(2)`
Adding equation (i) and (ii), we get
`2b = 4`
`b = 2`
Putting this value in equation (i), we get,
-a + 2 = 4
a = -2
Hence, the value of a and b are – 2 and 2 respectively.
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