Polynomials
Grade Class 10
Question:
<p><strong>Assertion (A):</strong> Polynomial x<sup>2</sup> + 4x has two real zeroes.<br />
<strong>Reason (R):</strong> Zeroes of the polynomial x<sup>2</sup> + ax (a <span class="math-tex">\(\neq\)</span> 0) are 0 and a.</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 zeroes of a polynomial are the values of x for which f(x) = 0, which can be found by factoring the expression into linear terms.
<p>Let f(x) = x<sup>2</sup> + 4x, Put f(x) = 0 to find its zeroes<br />
x<sup>2</sup> + 4x = 0<br />
x(x + 4) = 0<br />
x = 0, -4<br />
Since, there two zeroes are real<br />
hence, Assertion is true<br />
Let P(x) = x<sup>2</sup> + ax<br />
P(x) = 0 to find its zeroes<br />
x<sup>2</sup> + ax = 0<br />
x(x + a) = 0<br />
x = 0, -a are zeroes of P(x)<br />
hence, Reason is false.</p>
Correct Answer: C