Question

if (x-2)&(x-3) are factors of polynomial x cube -ax square +31x-b find a and b​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

${x}^{3} - a {x}^{2} + 31x - b = 0 \\ for \: factor \: x - 2 \\ x = 2 \\ {2}^{3} - a( {2}^{2} ) + 31(2) - b = 0 \\ 8 - 4a + 62 - b = 0 \\ 70 - 4a - b = 0 \\ - 4a - b = - 70 \\ - (4a + b) = - 70 \\ 4a + b = 70 \: \: \: equ \: (1) \\ \\ for \: factor \: x - 3 \\ x = 3 \\ {3}^{3} - a( {3}^{2} ) + 31(3) - b = 0 \\ 27 - 9a + 93 - b = 0 \\ 120 - 9a - b = 0 \\ - 9a - b = - 120 \\ - (9a + b) = - 120 \\ 9a + b = 120 \: \: \: \: equ \: (2) \\ \\ subtract \: equ \: (2) - (1) \\ 9a + b - 4a - b = 120 - 70 \\ 5a = 50 \\ a = \frac{50}{5} = 10 \\ \\ substitute \: a = 10 \: in \: equ \: (1) \\ 4a + b = 70 \\ 4(10) + b = 70 \\40 + b = 70 \\ b = 70 - 40 \\ b = 30$

a = 10 and b = 30

Hope you get your answer