Quadratic Equations
Equations with absolute values
Grade 11
Question:
<p>If \(a < 0\), then the value of \(x\) satisfying \(x^2 - 2a|x - a| - 3a^2 = 0\) is/are</p>
<p>(a) \(a(1 - \sqrt{2})\)</p>
<p>(b) \(a(1 + \sqrt{2})\)</p>
<p>(c) \(a(-1 - \sqrt{6})\)</p>
<p>(d) \(a(-1 + \sqrt{6})\)</p>
Step-by-Step Solution
Key Concept: Handle absolute value by considering cases: $x \geq a$ and $x < a$.
<p>Consider two cases based on the sign of $(x - a)$. When $a < 0$, analyze the absolute value equation by substituting $x - a$ and solving the resulting quadratic equations.</p>
Correct Answer: A, D