Question

If α and β are the zeroes of a polynomial 2x² + 7x + 5, write the value of α + β + αβ. [CBSE 2010]

Answer 1

By using the relationship between the zeros of the quadratic ploynomial.
We have,
Sum of zeroes = $\frac{-\left(\mathrm{coefficient}\mathrm{of}\mathit{}x\right)}{\mathrm{coefficent}\mathrm{of}{x}^2}$ and Product of zeroes = $\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficent}\mathrm{of}{x}^2}$
$$\begin{gathered} \therefore \alpha +\beta =\frac{-7}{2}\mathrm{and}\alpha \beta =\frac{5}{2} \\ \mathrm{Now},\alpha +\beta +\alpha \beta =\frac{-7}{2}+\frac{5}{2}=-1 \end{gathered}$$