Polynomials
Grade Class 10
Question:
<p>If <span class="math-tex">\(\alpha \)</span> and <span class="math-tex">\(\beta \)</span> are zeros of x<sup>2</sup> + 5x + 8, then the value of <span class="math-tex">\(( \alpha + \beta )\)</span>is</p>
<p style="display:inline">8</p>
<p style="display:inline">-8</p>
<p style="display:inline">5</p>
<p style="display:inline">-5</p>
Step-by-Step Solution
Key Concept: For a quadratic polynomial ax² + bx + c with zeros α and β, Vieta's formulas state that α + β = -b/a. Here, with x² + 5x + 8, the sum of zeros equals -5/1 = -5.
<p><span class="math-tex">$x^2 + 5x + 8$</span></p>
<p><span class="math-tex">$\alpha + \beta = \frac {-\text{Coefficient of x}}{\text{Coefficient of }x^2}$</span></p>
<p><span class="math-tex">$ = \frac{{ - 5}}{1}$</span></p>
<p>= -5</p>
Correct Answer: D