Polynomials
Grade Class 10
Question:
<p>If 5 is a zero of the quadratic polynomial, x<sup>2</sup> - kx - 15 then the value of k is</p>
<p style="display:inline">-2</p>
<p style="display:inline">-4</p>
<p style="display:inline">2</p>
<p style="display:inline">4</p>
Step-by-Step Solution
Key Concept: If a number is a zero of a polynomial, then substituting that value for x must result in the polynomial evaluating to zero.
<p>p(x) = x<sup>2</sup> - kx - 15.<br />
Given, 5 is zero of p(x)<br />
<span class="math-tex">$\therefore$</span> p(5) = 0<br />
<span class="math-tex">$\Rightarrow$</span> (5)<sup>2</sup> - k(5) - 15 = 0<br />
25 - 5k - 15 = 0<br />
-5k + 10 = 0<br />
k = <span class="math-tex">$\frac {10}{5}$</span><br />
k = 2</p>
Correct Answer: C