Polynomials
Grade Class 10
Question:
<p>The zeros of the polynomial <span class="math-tex">\(x^{2}-\sqrt{2} x-12\)</span> are</p>
<p style="display:inline">3, -1</p>
<p style="display:inline">3, 1</p>
<p style="display:inline"><span class="math-tex">\(3 \sqrt{2},-2 \sqrt{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\sqrt{2},-\sqrt{2}\)</span></p>
Step-by-Step Solution
Key Concept: Find the zeros of a quadratic polynomial by factorizing the expression through splitting the middle term into components that incorporate the radical coefficient.
<p><span class="math-tex">$x^{2}-\sqrt{2} x-12=x^{2}-3 \sqrt{2} x+2 \sqrt{2} x-12$</span><br />
<span class="math-tex">$=x(x-3 \sqrt{2})+2 \sqrt{2}(x-3 \sqrt{2})=$</span> <span class="math-tex">$(x-3 \sqrt{2})(x+2 \sqrt{2})$</span><br />
<span class="math-tex">$\therefore \quad x=3 \sqrt{2}$</span> or <span class="math-tex">$x=-2 \sqrt{2}$</span></p>
Correct Answer: C