Question

If one of the zeroes of the quadratic polynomial x² + bx + c is negative of the other, then

(a) b = 0 and c is positive
(b) b = 0 and c is negative
(c) b ≠ 0 and c is positive
(d) b ≠ 0 and c is negative

Answer 1

$$\begin{gathered} \left(\text{b}\right)\mathit{\text{b}}\text{=0 and}\mathit{\text{c}}\text{is negative} \\ \mathrm{Let}\alpha \text{and}-\alpha \text{be the zeroes of}{x}^2+bx+c. \\ \text{Then}\mathrm{\alpha }\text{+}(-\mathrm{\alpha })=-b \\ =>-b=0 \\ =>b=0 \\ \text{Also,}\mathrm{\alpha }\times (-\mathrm{\alpha })=c \\ =>-{\mathrm{\alpha }}^2=c \\ =>c\text{is negative, as}{\alpha }^2>0 \\ \therefore b=0\text{and}c\text{is negative}\text{.} \end{gathered}$$