Polynomials
Grade Class 10
Question:
<p>The number polynomials having zeroes as – 2 and 5 is</p>
<p style="display:inline">3</p>
<p style="display:inline">2</p>
<p style="display:inline">1</p>
<p style="display:inline">more than 3</p>
Step-by-Step Solution
Key Concept: A given set of zeroes defines an infinite family of polynomials of the form k(x² - Sx + P), where k is any non-zero real constant.
<p>The number polynomials having zeroes as –2 and 5 is more than 3. If ‘S’ is the sum and ‘P’ is the product of the zeroes then the corresponding family of quadratic polynomial is given by <span class="math-tex">\(p\left( x \right) = k\left( {{x^2} - {\text{S}}x + {\text{P}}} \right)\)</span>where <span class="math-tex">\(k\)</span> is any real number. Therefore putting different values of <span class="math-tex">\(k\)</span>, we can make more than 3 numbers of polynomials.</p>
Correct Answer: D