If $x = 2$ is a root of the polynomial $f(x) = 2x^2-3x + 7a$, find the value of $a$.

Given :

The given polynomial is $f(x) = 2x^2-3x + 7a$.

$x = 2$ is a root of the polynomial $f(x) = 2x^2-3x + 7a$.

To find :

We have to find the value of $a$.

Solution :

The zero of the polynomial is defined as any real value of $x$, for which the value of the polynomial becomes zero.

Therefore,

Zero of the polynomial $f(2)= 2(2)^2-3(2)+7a=0$

$2(4)-6+7a=0$

$7a=6-8$

$7a=-2$

$a=\frac{-2}{7}$

The value of $a$ is $\frac{-2}{7}$. 

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Updated on: 10-Oct-2022

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