Question:
<p>If <span class="math-tex">\(\alpha, \beta\)</span> are zeroes of the polynomial <span class="math-tex">\(3 x^{2}+14 x-5\)</span>, then the value of <span class="math-tex">\(3\left(\frac{\alpha+\beta}{\alpha \beta}\right)\)</span> is:</p>
<p style="display:inline"><span class="math-tex">\(-\frac{42}{5}\)</span></p>
<p style="display:inline"><span class="math-tex">\(-\frac{14}{5}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{42}{5}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{14}{5}\)</span></p>
Step-by-Step Solution
Key Concept: Use Vieta's formulas to relate the sum and product of roots directly to the polynomial's coefficients.
<p><span class="math-tex">$\frac{42}{5}$</span></p>
Correct Answer: C