Polynomials
Grade Class 10
Question:
<p><strong>Assertion (A):</strong> If the product of the zeroes of the quadratic polynomial x<sup>2</sup> + 3x + 5k is -10 then value of k is -2.<br />
<strong>Reason (R):</strong> Sum of zeroes of quadratic polynomial ax<sup>2</sup> + bx + c is -<span class="math-tex">\(\frac{b}{a}\)</span>.</p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: The coefficients of a quadratic polynomial are related to its zeroes via the formulas: Sum = -b/a and Product = c/a.
<p>Reason is true as we know that Sum of zeroes = -<span class="math-tex">$\frac{b}{a}$</span><br />
Also, we know that Product of zeroes = <span class="math-tex">$\frac{c}{a}$</span><br />
<span class="math-tex">$\Rightarrow$</span> <span class="math-tex">$\frac{5k}{1}$</span> = -10 <span class="math-tex">$\Rightarrow$</span> k = -2<br />
So, the Assertion is true. But Reason is not the correct explanation of assertion.<br />
</p>
Correct Answer: B