Question

If $\alpha ,\beta$ are the roots of the quadratic equation $(p^2+p+1)x^2+(p-1)x+p^2=0$ such that unity lies between the roots then the set of values of $p$ is:

• A. $\varphi$
• B. $pϵ(-\infty ,-1)U(0,\infty )$
• C. $pϵ(-1,0)$
• D. $(-1,1)$

Answer 1

The correct option is C $pϵ(-1,0)$

Given unity lies between the roots$\Rightarrow$f(1)<0(see diagram)

$\Rightarrow p^2+p+1+p-1+p^2<0$

$\Rightarrow p^2+p<0$

$\Rightarrow p(p+1)<0$

$\Rightarrow p\in (-1,0)$