If `x=2` and `x=0` are roots of the polynomial `f(x)=2x^3-5x^2+ax+bdot` Find the values of `a` and `bdot`

Explanation

To find the values of \( a \) and \( b \) for the polynomial \( f(x) = 2x^3 - 5x^2 + ax + b \) given that \( x = 2 \) and \( x = 0 \) are roots, we can follow these steps:

### Step 1: Identify the roots
Since \( x = 0 \) and \( x = 2 \) are roots, we can denote the third root as \( r \). The polynomial can be expressed in terms of its roots:
\[ f(x) = k(x - 0)(x - 2)(x - r) \]
where \( k \) is a constant.
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