Question

$\text{If}\alpha \text{and}\beta \text{are zeroes of the polynomial}2x^2+5x+1,\text{then find the value of}\alpha +\beta +\alpha \beta .$

Answer 1

Find the values of $\mathit{\alpha }\mathbf{+}\mathit{\beta }\mathbf{+}\mathit{\alpha }\mathit{\beta }$:

Here, the polynomial is $2x^2+5x+1$

Then, $a=2;b=5;c=1$

$$\begin{gathered} \begin{array}{cc}\alpha +\beta & =\frac{-b}{a}\\ & =\frac{-5}{2}\\ \alpha \beta & =\frac{c}{a}\\ & =\frac{1}{2}\end{array} \\ Therefore, \\ \begin{array}{cc}\alpha +\beta +\alpha \beta & =\frac{-5}{2}+\frac{1}{2}\\ & =\frac{-4}{2}\\ & =-2\end{array} \end{gathered}$$

Thus, the value of $\alpha +\beta +\alpha \beta$ is -2