CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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

Solution

The correct option is C Statement-1 is True, Statement-2 is False
Statement -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

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More



footer-image