Use the quadratic formula or graphing methods to -$$4 x ^ { 2 } 4 x + 4$$ A) $x \frac { 1 + \sqrt { 5 } } { 2 } \approx 1.618$ B) $\frac { 1 - \sqrt { 5 } } { 2 } \approx - 0.618

Question

Use the quadratic formula or graphing methods to -$$4 x ^ { 2 } > 4 x + 4$$ A) $x < \frac { 1 - \sqrt { 5 } } { 2 } \approx - 0.618$ or $x > \frac { 1 + \sqrt { 5 } } { 2 } \approx 1.618$ B) $\frac { 1 - \sqrt { 5 } } { 2 } \approx - 0.618 < x < \frac { 1 + \sqrt { 5 } } { 2 } \approx 1.618$ C) $x > \frac { 1 + \sqrt { 5 } } { 2 } \approx 1.618$ D) $x < \frac { 1 - \sqrt { 5 } } { 2 } \approx - 0.618$

Quizplus · Accepted Answer

First, rearrange the inequality to $4x^2 - 4x - 4 > 0$. Using the quadratic formula, $x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(4)(-4)}}{2(4)}$, we find the roots to be $x = \frac{1 \pm \sqrt{5}}{2}$. The inequality is satisfied outside these roots, leading to $x < \frac{1 - \sqrt{5}}{2}$ or $x > \frac{1 + \sqrt{5}}{2}$.

Use the Quadratic Formula or Graphing Methods to - 4x2>4x+44 x ^ { 2 } > 4 x + 44x2>4x+4

Use the Quadratic Formula or Graphing Methods to
- $4 x ^ { 2 } > 4 x + 4$