Polynomials
Grade Class 10
Question:
<p>If the sum and the product of zeroes of a quadratic polynomial are <span class="math-tex">\(2\sqrt 3\)</span> and 3 respectively, then a quadratic polynomial is:</p>
<p style="display:inline"><span class="math-tex">\(x^2-2 \sqrt{3} x-3\)</span></p>
<p style="display:inline"><span class="math-tex">\((x-\sqrt{3})^2\)</span></p>
<p style="display:inline"><span class="math-tex">\(x^2+2 \sqrt{3} x+3\)</span></p>
<p style="display:inline"><span class="math-tex">\(x^2+2 \sqrt{3} x-3\)</span></p>
Step-by-Step Solution
Key Concept: A quadratic polynomial is constructed by substituting the sum (S) and product (P) of zeroes into the general expression $x^2 - Sx + P$.
<p><span class="math-tex">\( \alpha+\beta=2 \sqrt{3} \)</span><br />
<span class="math-tex">\( \alpha \beta=3\)</span><br />
required quad. poly is<br />
<span class="math-tex">\( x^2-(\alpha+\beta) x+\alpha \beta=0 \)</span><br />
<span class="math-tex">\(x^2-(2 \sqrt{3}) x+3=0 \)</span><br />
<span class="math-tex">\(x^2-2 \sqrt{3} x+3=0 \)</span><br />
<span class="math-tex">\((x-\sqrt{3})^2=0 \)</span></p>
Correct Answer: B