First slide

Theory of expressions

Question

Let $f (x) = {ax}^{2} + bx + c$ . Consider the following diagram. Then

Moderate

A

c < 0
B

b > 0
C

a + b - c > 0
D

abc < 0

Solution

Let $f (x) = {ax}^{2} + bx + c$ .
From the diagram, we can see that a > 0, c < 0 and -[b(2a)] < 0. Hence, b > 0.
$∴ a + b - c > 0$

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