Determine the expression of the equation 2x^3-x^2+ax+b=0 if a solution is 1+i .

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We have the equation: 2x^3 - x^2 + ax + b = 0 with one of its solutions given as 1 + i.

Substituting x with 1 + i,

2*(1 + i)^3 - (1 + i)^2 + a(1 + i) + b = 0

=> 2*( 1 + 3i^2 + 3i + i^3) - 1 - i^2 - 2i + a + ai + b = 0

=> 2*( 1 - 3 + 3i - i) - 1 + 1 - 2i + a + ai + b = 0

=> 2*( - 2 + 2i ) - 2i + a + ai + b = 0

=> -4 + 4i - 2i + a + ai + b = 0

=> -4 + a + b + i( 2 + a) = 0

Equating the real and complex coefficients, we have

-4 + a + b = 0

2 + a = 0

=> a = -2

substituting a = 6 in -4 + a + b = 0

=> -4 - 2 + b = 0

=> b = 6

The required equation is 2x^3 - x^2 - 2x + 6 = 0

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