find a and b if x+1 and x+2 are factors of
[tex] {x}^{3} \: + 3 {x}^{2} \: - 2ax \: + b[/tex]
class - 9
[tex] {x}^{3} \: + 3 {x}^{2} \: - 2ax \: + b[/tex]
class - 9
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Let p(x) = x³ + 3x² - 2ax + b
Factors = x + 1 and x + 2
Thus zeros = (-1) and (-2)
Thus p(-1) = 0
=> (-1)³ + 3(-1)² - 2a(-1) + b = 0
=> - 1 + 3 + 2a + b = 0
=> 2a + b = - 2 ------- (1)
Similarly p(-2) = 0
=> (-2)³ + 3(-2)² - 2a(-2) + b = 0
=> -8 + 12 + 4a + b = 0
=> 4a + b = -4 --------(2)
Subtract (2) from (1)
=> 2a + b - (4a + b) = - 2 - (-4)
=> - 2a = 2
=> a = - 1 <<<<<< Answer
Thus
=> 2a + b = - 2
=> b = 0 <<<<< Answer
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