Question

If α, β be the zeros of the polynomial x² − 8x + k such that α² + β² = 40, then k = ?

(a) 6
(b) 9
(c) 12
(d) −12

Answer 1

$$\begin{gathered} \left(\text{c}\right)12 \\ \text{Since}\mathrm{\alpha }\mathrm{and}\mathrm{\beta }\text{are the zeroes of}{x}^2-8x+k,\text{we have:} \\ \mathrm{\alpha }+\mathrm{\beta }=8\text{and}\alpha \beta \text{=}k \\ \text{Also, it is given that}{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2=40. \\ \text{Now,}{(\mathrm{\alpha }+\mathrm{\beta })}^2={\mathrm{\alpha }}^2+{\mathrm{\beta }}^2+2\mathrm{\alpha \beta } \\ =>8^2=40+2k \\ =>2k=24 \\ =>k=12 \end{gathered}$$