Question

Solve the polynomial inequality. Express the solution set in interval notation.

$16x^2<15x+1$

• A. $(-\infty ,-1]\cup (\frac{1}{16},\infty )$
• B. $(-1,\frac{1}{16})$
• C. $(-\frac{1}{16},1)$
• D. $(-\infty ,\frac{1}{16})\cup (1,0)$

Answer 1

The correct option is C $(-\frac{1}{16},1)$

$16x^2<15x+1$
$\Rightarrow 16x^2-15x-1<0$
$\Rightarrow 16x^2-16x+x-1<0$
$\Rightarrow 16x(x-1)+1(x-1)<0$
$\Rightarrow (16x+1)(x-1)<0$
$\Rightarrow x\in (\frac{-1}{16},1)$