We are given a linear equation in one variable: \( ax + b = 0 \)
Step 1: Subtract \( b \) from both sides of the equation \( ax = -b \)
Step 2: Divide both sides by \( a \) to isolate \( x \) \[ x = \frac{-b}{a} \]
The correct option is (D): \(-\frac{b}{a}\)
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - ax - b = 0 \) with \( \text{Im}(\alpha) < \text{Im}(\beta) \). Let \( P_n = \alpha^n - \beta^n \). If \[ P_3 = -5\sqrt{7}, \quad P_4 = -3\sqrt{7}, \quad P_5 = 11\sqrt{7}, \quad P_6 = 45\sqrt{7}, \] then \( |\alpha^4 + \beta^4| \) is equal to: