Question

What is the range of x for which the expression 19x - $2x^2$ - 35 is positive?

• A. x < 7
• B. $x>\frac{5}{2}$
• C. $\frac{5}{2}\le x\le 7$
• D. $\frac{5}{2}<x<7$

Answer 1

The correct option is D $\frac{5}{2}<x<7$

Let y denote the given expression
y = -($2x^2$ - 19x + 35) = -(2x - 5) (x - 7)
= (2x - 5) (7 - x) = 2 $(x-\frac{5}{2})$ (7 - x)
For y to be positive
i.e.,$(x-\frac{5}{2})$ (x - 7) < 0
$\therefore \frac{5}{2}$ < x < 7