question_answer

If the roots of the quadratic equation \[3{{x}^{2}}+2x+{{a}^{2}}-a=0\]in\[x\]are of opposite signs, then a lies in the interval

A)                              

B)  \[(-\infty ,0)\]

C)  \[(-1,0)\]           

D)         \[(0,1)\]

E)  \[(1,3)\]

Correct Answer: D

Solution :

\[3{{x}^{2}}+2x+{{a}^{2}}-a=0\] The condition for a quadratic equation have both roots are an opposite sign is constant term\[<0\] \[\Rightarrow \]               \[({{a}^{2}}-a)<0\] \[\Rightarrow \]               \[a(a-1)<0\] \[\Rightarrow \]               \[a\in (0,1)\]