If [( 1 - p )] is a root of quadratic equation [x^2 + px + ( 1 - p ) = 0] then its root ar…

Question

If $$\left( {1 - p} \right)$$   is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$  then its root are

Accepted Answer

Let the second root be $$\alpha .$$

Then $$\alpha  + \left( {1 - p} \right) =  - p \Rightarrow \alpha  =  - 1$$

Also $$\alpha .\left( {1 - p} \right) = 1 - p$$

$$ \Rightarrow \left( {\alpha  - 1} \right)\left( {1 - p} \right) = 0$$

$$ \Rightarrow p = 1$$ [as $$\alpha  =  - 1$$]

$$\therefore$$ Roots are $$\alpha  =  - 1$$ and $p-1=0$

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