Question

find a and b if x+1 and x+2 are factors of
${x}^{3} \: + 3 {x}^{2} \: - 2ax \: + b$
class - 9

Answer 1

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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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Hope this helps ✌️