Question

Graph of $y=a{x}^2+bx+c=0$ is given. What conclusions can be drawn from this graph?

• A. $a>0$
• B. $b<0$
• C. $c<0$
• D. $b^2-4ac>0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $a>0$
B $b<0$
C $c<0$
D $b^2-4ac>0$

Since parabola is upward $a>0$
Curve is crossing x-axis at two points $\Rightarrow$ roots are real $\Rightarrow b^2-4ac>0$
Roots are of opposite signs $c/a<0\Rightarrow c<0$
Also magnitude of +ve root is larger $\Rightarrow$ sum of roots $>0$
$\Rightarrow -b/2a>0\Rightarrow b<0$
Hence all the options are correct.