Question

If the zeros of a quadratic polynomial ax² + bx + c are both negative, then a, b, c will have the same sign.

(a) True
(b) False

Answer 1

$$\begin{gathered} \left(a\right)\mathrm{True} \\ \text{Let}\mathrm{\alpha }\text{and}\mathrm{\beta }\text{be the negative zeroes of}a{x}^2+bx+c. \\ \mathrm{Then}\mathrm{\alpha }+\mathrm{\beta }=\frac{-b}{a}<0\text{and}\mathrm{\alpha \beta }\text{=}\frac{c}{a} \\ =>\frac{b}{a}>0\text{and}\frac{c}{a}>0 \\ =>a,b,c\text{have the same sign}\text{.} \\ \therefore \mathrm{The}\mathrm{g}\text{iven statement is true}\text{.} \end{gathered}$$