If α and β(α<β)  are the roots of the equation x2+bx+c=0,where c<0

If α and β(α<β)  are the roots of the equation x2+bx+c=0,where c<0<b,then 

  1. A

    0<α<β

  2. B

    α<0<β<|α|

  3. C

    α<β<0

  4. D

    α<0<|α|<β

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    Solution:

    Sinceα , β are the roots of the equation x2+bx+c=0.Here,D=b24c>0 because c<0<b. so, roots are real and unequal. 
    Now ,α+β=b<0 and αβ=c<0 
     One root is positive and the other is negative, then the negative root being numerically bigger. As,α<β , α is the negative root while βis the positive root. so|α|>β
    and  α<0<β

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