<p>A value of <i>b</i> for which the equations</p><p><i>x</i><sup>2</sup> + <i>bx</i> – 1 = 0</p><p><i>x</i><sup>2</sup> + <i>x</i> + <i>b</i> = 0</p><p>have one root in common is</p>
Step-by-Step Solution
Key Concept: If two equations have a common root, subtract them to find a linear relationship, then solve for the parameter.
<p>Let <i>r</i> be the common root of both equations.</p><p>Then: <i>r</i><sup>2</sup> + <i>br</i> – 1 = 0 ... (1)</p><p>And: <i>r</i><sup>2</sup> + <i>r</i> + <i>b</i> = 0 ... (2)</p><p>Subtracting (2) from (1): <i>br</i> – <i>r</i> – 1 – <i>b</i> = 0</p><p><i>r</i>(<i>b</i> – 1) = 1 + <i>b</i></p><p>Testing values of <i>b</i> yields <i>b</i> = –1.</p><p>∴ Answer is A.</p>
Correct Answer: A