Question:
If $x=2$ is a root of the polynomial $f(x)=2 x^{2}-3 x+7 a$, Find the value of a
Solution:
We know that, $f(x)=2 x^{2}-3 x+7 a$
Given that x = 2 is the root of f(x)
Substitute the value of x in f(x)
$f(2)=2(2)^{2}-3(2)+7 a$
= (2 * 4) - 6 + 7a
= 8 - 6 + 7a
= 7a + 2
Now, equate 7a + 2 to zero
⟹ 7a + 2 = 0
⟹ 7a = - 2
⟹ a = - 27
The value of a = - 2/7
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