Question

Given that $x$ is a real number satisfying $\frac{5x^2-26x+5}{3x^2-10x+3}<0$, then

• A. $x<\frac{1}{5}$
• B. $\frac{1}{5}<x<3$
• C. $x>5$
• D. $\frac{1}{5}<x<\frac{1}{3}$ or $3<x<5$

Answer 1

Answer: (D)

$\frac{1}{5}<x<\frac{1}{3}$ or $3<x<5$

$\frac{5x(x-5)-(x-5)}{3x(x-3)-(x-3)}<0$

$\Rightarrow \frac{(5x-1)(x-5)}{(3x-1)(x-3)}<0$

Here we can use wavy curve method to determine the sign of the function.

We clearly get option D as the range of values for which given expression is negative.