Question

The graph of a quadratic polynomial $y=a x^2+b x+c$ is as shown in the adjacent figure. Which of the following quantities is(are) positive?

• A. $b-c$
• B. $b c$
• C. $c - a$
• D. $a b^2$

Answer 1

Answer: (C)

$a <0 ;-\frac{ b }{ a }<0 \Rightarrow b <0 ; \frac{ c }{ a }<0 \Rightarrow \quad c >0$
now $b - c = (- ve) - (+ ve)$ must be negative
$bc = (-) (+ve)$ must be negative
$ab^2 = (-) (+ve)$ must be negative
$c - a = (+) - (- ) $ must be positive.