<p>Given the equation \(x^2 - 1154x + 1 = 0\) with roots \(a\) and \(b\), find \(a + b\) and \(ab\).</p>
Step-by-Step Solution
Key Concept: Apply Vieta's formulas directly to extract the sum and product of roots from the quadratic equation.
<p><strong>Step 1:</strong> For the quadratic equation $x^2 - 1154x + 1 = 0$, apply Vieta's formulas:</p><p>$a + b = 1154$ (sum of roots = negative coefficient of x / coefficient of $x^2$)</p><p>$ab = 1$ (product of roots = constant term / coefficient of $x^2$)</p><p>∴ $a + b = 1154$ and $ab = 1$.</p>
Correct Answer: 1154, 1