Question

The zeros of the quadratic polynomial x2 + kx + k, where k > 0

(a) are both positive
(b) are both negative
(c) are always equal
(d) are always unequal

Answer 1

$$\begin{gathered} \left(\text{b}\right)\mathrm{are}\mathrm{both}\mathrm{negative} \\ \text{Let}\mathrm{\alpha }\text{and}\mathrm{\beta }\text{be the zeroes of}{x}^2+kx+k. \\ \text{Then}\alpha \text{+}\beta \text{=}-k\text{and}\alpha \times \beta \text{=}k \\ \text{This is possible only when}\alpha \text{and}\beta \text{are both negative}\text{.} \end{gathered}$$