A resistance thermometer reads `R=20.0Omega, 27.5 Omega,` and `50.0 Omega` at the ice point `(0^@C)`, the steam point `(100^@C)` and the zinc point `(420^@C)` respectively. Assuming that the resistance varies with temperature as `R_Theta=R_0(1+alphaTheta+betaTheta^2)` , find the values of `R_0`, `alpha` and `beta`. Here `Theta` represents the temperature on Celsius scale.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Set up the equations based on the given data

We know that the resistance \( R_\Theta \) varies with temperature \( \Theta \) according to the formula:

\[
R_\Theta = R_0(1 + \alpha \Theta + \beta \Theta^2)
...