The graph of a quadratic polynomial y=a x2+b x+c is as shown in the adjacent figure. Which of the following quantities is(are) positive?

Question

The graph of a quadratic polynomial y=a x2+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 b2

Tardigrade Admin · Accepted Answer

a <0 ;-( b / a )<0 ⇒ b <0 ; ( c / a )<0 ⇒ c >0 now b - c = (- ve) - (+ ve) must be negative bc = (-) (+ve) must be negative ab2 = (-) (+ve) must be negative c - a = (+) - (- ) must be positive.

Q. 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?

$b - c$

$b c$

$c - a$

$a b^{2}$

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

Q. The graph of a quadratic polynomial y=ax2+bx+c is as shown in the adjacent figure. Which of the following quantities is(are) positive?

b−c

bc

c−a

ab2