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Question

# Statement 1 : If f(x)=ax2+bx+c, where a>0,c<0 and b∈R, then roots of f(x)=0 must be real and distinct .Statement 2 : If f(x)=ax2+bx+c, where a>0,b∈R,b≠0 and the roots of f(x)=0 are real and distinct, then c is necessarily negative real number .

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
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C
Statement-1 is True, Statement-2 is False
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D
Statement-1 is False, Statement-2 is True
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Solution

## The correct option is C Statement-1 is True, Statement-2 is FalseStatement -1 b2−4ac>0 {Since a>0,c<0}∴ Roots are real and distinct∴ Statement -1 is true .Statement -2 Since the roots are real and distinct∴b2−4ac>0 i.e. c<b24aThus, c is not necessarily negative∴ Statement -2 is false .

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