Find the value of $a$ such that $(x - 4)$ is a factor of $5x^3 - 7x^2 - ax - 28$.

Given:

Given expression is $5x^3 - 7x^2 - ax - 28$.

$(x - 4)$ is a factor of $5x^3 - 7x^2 - ax - 28$.

To do:

We have to find the value of $a$.

Solution:

We know that,

If $(x-m)$ is a root of $f(x)$ then $f(m)=0$.

Therefore,

$f(4)=0$

$\Rightarrow 5(4)^3-7(4)^2-a(4)-28=0$

$\Rightarrow 5(64)-7(16)-4a-28=0$

$\Rightarrow 320-112-4a-28=0$

$\Rightarrow 4a=180$

$\Rightarrow a=\frac{180}{4}=45$

The value of $a$ is $45$.   

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Updated on: 10-Oct-2022

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