4. Verify the following

If \(\alpha\), \(\beta\) and \(\gamma\) are the zeroes of the cubic polynomial $3x^3-10x^2+9x-2$, check whether $1,2,\frac{1}{3}$  are the zeroes of the cubic polynomial and verify the relation between the zeroes and the coefficients of the polynomial.

 

Answer:

 

Let $1,2,\frac{1}{3}$ be the \(\alpha, \beta, \gamma\) of the given cubic polynomial.

 

Then, \(p(\alpha) =\)

 

\(p(\beta) = \)

 

\(p(\gamma) =\)

 

\(\alpha + \beta + \gamma\)=\(\neq \)\( -\frac{b}{a}\)

 

 \(\alpha \beta + \beta \gamma + \gamma \alpha\)=\(\neq \)\( \frac{c}{a}\)