* if x+1 and x+2 are the factors of ax3 + bx2 +17 +10 find a and b
* if x2 - 3x + 2 is a factor of x3 - x2 - px +q ,find pand q
* find the value of a and b so that the x3 -ax2 - 13x + b has x-1 and x+3 as factor
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1)
x+1 and x+2 are factors of P(x) = a x³ + b x² + 17 x + 10
P(-1) = - a + b - 17 + 10 = 0 => a + b = 7
P(-2) = -8 a + 4 b - 34 + 10 = 0 => b - 2 a = 6
subtract one from the second, a = 1/3 b = 20/3
2)
x² - 3 x + 2 = (x - 2) (x -1) are factors of P(x) = x³ - x² - p x + q
so P(2) = 0 = 8 - 4 - 2 p + q => 2p - q = 4
P(1) = 0 = 1 - 1 - p + q => p = q
solving them, q = p = 4
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3
P(x) = x³ - a x² - 13 x + b has x - 1 and x+3 as the factors.
P(1) = 0 = 1 - a - 13 + b => - a + b = 12
P(-3) = 0 = -27 - 9 a + 39 + b => b - 9 a = -12
solving them, we get a = a = 3 b = 15
x+1 and x+2 are factors of P(x) = a x³ + b x² + 17 x + 10
P(-1) = - a + b - 17 + 10 = 0 => a + b = 7
P(-2) = -8 a + 4 b - 34 + 10 = 0 => b - 2 a = 6
subtract one from the second, a = 1/3 b = 20/3
2)
x² - 3 x + 2 = (x - 2) (x -1) are factors of P(x) = x³ - x² - p x + q
so P(2) = 0 = 8 - 4 - 2 p + q => 2p - q = 4
P(1) = 0 = 1 - 1 - p + q => p = q
solving them, q = p = 4
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3
P(x) = x³ - a x² - 13 x + b has x - 1 and x+3 as the factors.
P(1) = 0 = 1 - a - 13 + b => - a + b = 12
P(-3) = 0 = -27 - 9 a + 39 + b => b - 9 a = -12
solving them, we get a = a = 3 b = 15
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