Polynomials
Grade Class 10
Question:
<p><strong>Assertion:</strong> <span class="math-tex">\((2-\sqrt{3})\)</span> is one zero of the quadratic polynomial then other zero will be <span class="math-tex">\((2+\sqrt{3})\)</span>.<br />
<strong>Reason:</strong> Irrational zeros (roots) always occurs in pairs.</p>
<p style="display:inline">Assertion and reason both are correct statements and reason is correct explanation for assertion.</p>
<p style="display:inline">Assertion and reason both are correct statements but reason is not correct explanation for assertion.</p>
<p style="display:inline">Assertion is correct statement but reason is wrong statement.</p>
<p style="display:inline">Assertion is wrong statement but reason is correct statement.</p>
Step-by-Step Solution
Key Concept: Irrational zeros of a quadratic polynomial occur in conjugate pairs, meaning if one zero is a - sqrt(b), the other must be a + sqrt(b).
<p>As irrational roots/zeros always occurs in pairs, therefore, when one zero is <span class="math-tex">$(2-\sqrt{3})$</span> then other will be <span class="math-tex">$(2+\sqrt{3})$</span>. So, both Assertion and Reason are correct and Reason explains Assertion.</p>
Correct Answer: A