Question:
<p>The sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is</p>
<p style="display:inline">x<sup>2</sup> - 3x -10</p>
<p style="display:inline">x<sup>2</sup> - 3x + 10</p>
<p style="display:inline">x<sup>2</sup> + 3x + 10</p>
<p style="display:inline">x<sup>2</sup> + 3x -10</p>
Step-by-Step Solution
Key Concept: A quadratic polynomial is constructed using the standard form x² - (sum of zeros)x + (product of zeros).
<p>Given, sum and the product of the zeros of a quadratic polynomial are 3 and -10 respectively<br />
i,e. <span class="math-tex">$(\alpha+\beta) = 3$</span> and <span class="math-tex">$\alpha \beta = -10$</span><br />
Therefore, required polynomial is<br />
<span class="math-tex">$x^{2}-(\alpha+\beta) x+\alpha \beta=x^{2}-3 x-10$</span></p>
Correct Answer: A