If `x=4/3` is a root of the polynomial `f(x)=6x^3-11 x^2+k x-20 ,` find the value of `k`

Explanation

To find the value of \( k \) in the polynomial \( f(x) = 6x^3 - 11x^2 + kx - 20 \) given that \( x = \frac{4}{3} \) is a root, we can follow these steps:

### Step 1: Substitute the root into the polynomial
Since \( x = \frac{4}{3} \) is a root, we know that \( f\left(\frac{4}{3}\right) = 0 \). Therefore, we substitute \( x = \frac{4}{3} \) into the polynomial:

\[ f\left(\frac{4}{3}\right) = 6\left(\frac{4}{3}\right)^3 - 11\left(\frac{4}{3}\right)^2 + k\left(\frac{4}{3}\right) - 20 = 0 \]
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