Question

For what value of a is p(x)= 4x3+ax2- x-1 exactly divisible by g(x)= 2x+1

Answer 1

Answer:

$\red { value \: of \: a }\green {= 4}$

Step-by-step explanation:

$Given \: p(x) = 4x^{3} + ax^{2} - x - 1 ,\: exactly\\divisible \: by \: g(x) = 2x + 1$

$If \: p(x) \: is \: exactly \: Divisible \: by \: g(x) \\then \: the \: the \: remainder \: p\left(\frac{-1}{2}\right) = 0$

$\implies 4\left(\frac{-1}{2}\right)^{3} + a\left(\frac{-1}{2}\right)^{2} - \left(\frac{-1}{2}\right) - 1 = 0$

$\implies 4 \times \frac{-1}{8} + a\times \frac{1}{4} + \frac{1}{2} - 1 = 0$

$\implies \frac{-1}{2} + \frac{a}{4} +\frac{1}{2} - 1 = 0$

$\implies \frac{a}{4} = 1$

$\implies a = 4$

Therefore.,

$\red { value \: of \: a }\green {= 4}$

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