find the value of k if 2x-3 is a factor of 2x^3+9x^2+x+k?
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find the value of k if 2x-3 is a factor of 2x^3+9x^2+x+k?
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Step-by-step explanation:
2x-3 =0
2x = 3
x = 3/2
2x^3 + 9x^2 + x + k = 0
2(3/2)^3 + 9(3/2)^2 + (3/2) + k = 0
2(27/8) + 9(9/4) + (3/2) + k = 0
(27/4) + (81/4) + (6/4) + k = 0
( 27+81+6 ) / 4 + k = 0
(114/4) + k = 0
(57/2) + k = 0
k = -(57/2)