Find the value of a and
b so that x +1 and X - 1 are factors of X^4+ ax^3 + 2x^2 - 3x + b
5.
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Answer:
if x +1 is a factor, then if -1 is substituted in place of x, then the polynomial = 0
So, (-1)⁴ + a(-1)³ + 2(-1)² -3(-1) + b = 0
1 - a + 2 + 3 + b = 0
b + 6 = a - - - - -(i)
Similarly, if x - 1 is a factor, p(1) = 0
1⁴ + a(1)³ + 2(1)² - 3(1) + b = 0
1 + a + 2 - 3 + b = 0
a + b = 0
From equation (i), b + 6 + b = 0
2b = -6
b = -3
Substituting this into a + b = 0,
a + (-3) = 0
a = 3
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