A) both roots are greater than \[\frac{-b}{2a}\]
B) both roots are less than\[\frac{-b}{2a}\]
C) one of the roots exceeds\[\frac{-b}{2a}\]
D) None of the above
Correct Answer: C
Solution :
Since, the roots of the given equation are \[\alpha =\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}\] and \[\beta =\frac{-b+\sqrt{{{b}^{2}}-4ac}}{2a}\] Since,\[\alpha \]and\[\beta \]are real and distinct. Then, \[{{b}^{2}}-4ac>0\] Now, if\[a>0,\]then \[\beta >\frac{-b}{2a}\] and if \[a<0,\]then \[\alpha <\frac{-b}{2a}\] Thus, one of the roots exceeds\[\frac{-b}{2a}\]
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