The roots of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{a}\in {\mathbf{R}}^{+}$, are two consecutive odd positive integers. Then

Let roots be 2k- 1 an $2k+1,k\in N$
$\text{ Then sum of roots }=4k=-\frac{b}{a}\text{. }$

Since $a\in {\mathit{R}}^{+},b<0.\text{ As }k\ge 1$
we have $-b=4ak\ge 4a$
Hence $\left|b\right|\ge 4a,[b<0\Rightarrow |b|=-b]$