Question

# Statement 1 :  If $$f(x)=ax^2+bx+c$$, where $$a > 0, c < 0$$ and $$b \in R$$, then roots of $$f(x)=0$$ must be real and distinct .Statement 2 :  If $$f(x)=ax^2+bx+c,$$ where $$a > 0, b \in R, b \neq 0$$ 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
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True

Solution

## The correct option is C Statement-1 is True, Statement-2 is FalseStatement -1  $$b^2-4ac > 0$$ {Since $$a > 0, c < 0$$}$$\therefore$$ Roots are real and distinct$$\therefore$$ Statement -1 is true .Statement -2  Since the roots are real and distinct$$\therefore b^2 -4ac > 0$$  i.e.  $$c < \displaystyle \frac{b^2}{4a}$$Thus, c is not necessarily negative$$\therefore$$ Statement -2 is false .Mathematics

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