Polynomials
Grade Class 10
Question:
<p>If one root of the polynomial f(x) = 3x<sup>2</sup> + 11x + p is reciprocal of the other, then the value of p is</p>
<p style="display:inline">-3</p>
<p style="display:inline">0</p>
<p style="display:inline">3</p>
<p style="display:inline"><span class="math-tex">\(\frac 13\)</span></p>
Step-by-Step Solution
Key Concept: When the roots of a quadratic equation are reciprocals, their product is 1, which implies the constant term must be equal to the leading coefficient.
<p>Let one root be q.<br />
<span class="math-tex">$\therefore$</span> Other root = <span class="math-tex">$\frac 1 q$</span><br />
<span class="math-tex">$\Rightarrow$</span> q <span class="math-tex">$\times$</span> <span class="math-tex">$\frac 1 q$</span> = <span class="math-tex">$\frac p 3$</span> <span class="math-tex">$\Rightarrow$</span> 1 = <span class="math-tex">$\frac p 3$</span> <span class="math-tex">$\Rightarrow$</span> p = 3</p>
Correct Answer: C