Find the roots of the given equation: contexto.140 3 years ago We have, as Hence, and are the roots of the given equation.
![\begin{array}{l} x^{2} \times\left[-\left(4 b^{2}-a^{2}\right)\right]=-\left(4 b^{2}-a^{2}\right) x^{2}=(2 b-a) x \times[-(2 b+a) x] \\ \therefore x^{2}-2 a x-\left(4 b^{2}-a^{2}\right)=0 \\ \Rightarrow x^{2}+(2 b-a) x-(2 b+a) x-(2 b-a)(2 b+a)=0 \\ \Rightarrow x[x+(2 b-a)]-(2 b+a)[x+(2 b-a)]=0 \\ \Rightarrow[x+(2 b-a)][x-(2 b+a)]=0 \\ \Rightarrow x+(2 b-a)=0 \text { or } x-(2 b+a)=0 \\ x=-(2 b-a) \text { or } x=2 b+a \\ \Rightarrow x=a-2 b \text { or } x=a+2 b \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8d7dadf031fae6c664d8a5363aad321e_l3.png "Rendered by QuickLaTeX.com")
