Find the values of p and q such that f(x) =x4-px2+q leaves remainder 3x+4 when divided by x2-3x+2.

Dear Student,
Please find below the solution to the asked query:

x2-3x+2=x2-2x-x+2=xx-2-1x-2=x-1x-2Dividend=Divisor ×Quotient+Remainderx4-px2+q=x2-3x+2×Quotient+3x+4x4-px2+q=x-1x-2×Quotient+3x+4Put x=11-p+q=0×Quotient+3+41-p+q=7p-q=-6...iPut x=216-4p+q=0×Quotient+6+416-4p+q=10-4p+q=-6...iii+iip-q-4p+q=-6-6-3p=-12p=4Put in i4-q=-6q=10

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