Polynomials
Grade Class 10
Question:
<p>A quadratic polynomial whose zeros are <span class="math-tex">\(\frac{3}{5}\)</span> and <span class="math-tex">\(\frac{-1}{2},\)</span> is</p>
<p style="display:inline">10x<sup>2</sup> - x -3</p>
<p style="display:inline">10x<sup>2</sup> - x + 3</p>
<p style="display:inline">10x<sup>2</sup> + x + 3</p>
<p style="display:inline">10x<sup>2</sup> + x - 3</p>
Step-by-Step Solution
Key Concept: A quadratic polynomial with zeros α and β is represented by k[x² - (α + β)x + αβ], where k is a non-zero scaling factor.
<p><span class="math-tex">$\alpha+\beta=\left(\frac{3}{5}-\frac{1}{2}\right)=\frac{1}{10}, \alpha \beta=\frac{3}{5} \times\left(\frac{-1}{2}\right)=\frac{-3}{10}$</span><br />
Required polynomial is <span class="math-tex">$x^{2}-\frac{1}{10} x-\frac{3}{10}$</span>, i.e., 10x<sup>2</sup> - x - 3</p>
Correct Answer: A