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  4. If the roots of the quadratic equation 3x2+2x+a2-a=0 in x are of opposite signs, then a lies in the interval

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Q. 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

KEAMKEAM 2011Complex Numbers and Quadratic Equations

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) $

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