Question

If the coefficient of $x^2$ and constant term are interchanged, then

• A. $P$ & $Q$ remains same
• B. $P$ and $Q$ are interchanged
• C. $P$ changes by set $Q$ but $R$ does not change
• D. None of these

Answer 1

The correct option is A $P$ & $Q$ remains same

By change of coefficient of $x^2$ and constant term with each other, we have

$(1+8m)x^2-2(1+3m)+(1+m)=0$

$\therefore P=$ set of those value for which $\alpha \beta >0$

$\Rightarrow \frac{(1+m)}{1+8m}>0$

$\Rightarrow mϵ(-\infty ,-1)\cup (\frac{-1}{8},\infty )$

$\therefore Q=$ set of those points for which $\beta \beta <0=(-1,\frac{-1}{8})$

$\therefore P$ and $Q$ remains same.

Hence choice $\left(a\right)$ is correct answer.