The sum of the non-real roots of $\left(p^2+p-3\right)\left(p^2+p-2\right)-12=0$ is

The sum of the non-real roots of $\left(p^2+p-3\right)\left(p^2+p-2\right)-12=0$ is
  1. 1
  2. -1
  3. 6
  4. -6

Solution

Given equation is $ \left(P^2+P-3\right)\left(P^2+P-2\right)-12=0 $ Let $y=P^2+P-2$ $ \begin{array}{lr} \therefore & y(y-1)-12=0 \\ \Rightarrow & y^2-y-12=0 \\ \Rightarrow & (y-4)(y+3)=0 \\ \Rightarrow & y-4=0 \text { as } y+3=0 \\ \Rightarrow & P^2+P-6=0 \text { as } P^2+P+1=0 \end{array} $ For imaginary (non-real roots) $ P^2+P+1=0 $ $\therefore$ Sum of non-real roots $=-1$

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

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