If (2x+1) is a factor of 6x3 + 5x2 + ax - 2 , find the value of a .

x3 - cube
x2 - square

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Solution

Let f(x) = 6x³ + 5x² + ax - 2

As (2x + 1) is a factor of the given ploynomial, so at 2x+1=0 ⇒ x= -1/2, f(x) becomes zero.

putting x= -1/2 in the polynomial, we get

f(-1/2) = 6(-1/2)³ + 5(-1/2)² + a(-1/2) -2 = 0

⇒ - 3/4 + 5/4 -a/2 -2 = 0

⇒ a/2 = (-3+5-8)/4

⇒ a/2 = -3/2

⇒ a = -3 Ans.

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