Mathematics - Quadratic Equation Question with Solution | TestHub

The given relation can be written as $\left(a^2{p}^2-2abp+b^2\right)+\left(b^2{p}^2+c^2-2bpc\right)+$ $\left(c^2{p}^2+d^2-2pcd\right)\le 0$ or $(ap-b{)}^2+(bp-c{)}^2+(cp-d{)}^2\le 0$ ...(1) Since $a,b,\mathrm{c},d$ and $p$ are all real, the inequality (1) is possible only when each of factor is zero. i.e., $ap-b=0,bp-c=0$ and $cp-d=0$ or $p=\frac{b}{a}=\frac{c}{b}=\frac{d}{c}$ or $a,b,c,d$ are in G.P.