Question

6) write the nature of roots of quadratic equation:

b) x²- b² - a (2x- a) = 0

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{is}, \\ {x}^2-b^2-a\left(2x-a\right)=0 \\ \Rightarrow x^2-2ax+\left(a^2-b^2\right)=0 \\ \mathrm{Now},A=1;B=-2a;C=\left(a^2-b^2\right) \\ D=B^2-4AC={\left(-2a\right)}^2-4\left(1\right)\left(a^2-b^2\right)=4a^2-4a^2+b^2=b^2 \\ \mathrm{Now},b^2⩾0 \\ \mathrm{So},D⩾0 \\ \mathrm{Hence},\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{are}\mathbf{real}. \end{gathered}$$