Find the value of 'a' for which 2x3+ax2+11x+a+3 is exactly divisible by 2x-1
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Heya !!
( 2x - 1 ) is a factor of the given polynomial 2X³ + AX² + 11X + A + 3.
( 2X - 1 ) = 0
2X = 1
X = 1/2.
P ( X ) = 2X³ + AX² + 11X + A + 3
P (1/2) = 2 × (1/2)³ + A × (1/2)² + 11 × 1/2 + A + 3
=> 2 × 1/8 + A × 1/4 + 11/2 + A + 3 = 0
=> 1/4 + A/4 + 11/2 + A + 3 = 0
=> 1 + A + 22 + 4A + 12 = 0
=> 5A + 35 = 0
=> 5A = -35
=> A = -7
( 2x - 1 ) is a factor of the given polynomial 2X³ + AX² + 11X + A + 3.
( 2X - 1 ) = 0
2X = 1
X = 1/2.
P ( X ) = 2X³ + AX² + 11X + A + 3
P (1/2) = 2 × (1/2)³ + A × (1/2)² + 11 × 1/2 + A + 3
=> 2 × 1/8 + A × 1/4 + 11/2 + A + 3 = 0
=> 1/4 + A/4 + 11/2 + A + 3 = 0
=> 1 + A + 22 + 4A + 12 = 0
=> 5A + 35 = 0
=> 5A = -35
=> A = -7
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