Polynomials
Grade Class 10
Question:
<p>A quadratic polynomial, whose zeros are 5 and - 8 is</p>
<p style="display:inline">x<sup>2</sup> + 13x - 40</p>
<p style="display:inline">x<sup>2</sup> - 3x - 40</p>
<p style="display:inline">x<sup>2</sup> + 3x - 40</p>
<p style="display:inline">x<sup>2</sup> + 4x - 3</p>
Step-by-Step Solution
Key Concept: A quadratic polynomial with zeros α and β is given by the formula p(x) = k[x^2 - (α+β)x + αβ].
<p>Let <span class="math-tex">\(\alpha\)</span> and <span class="math-tex">\(\beta\)</span>, zeroes of the quadratic polynomials where, <span class="math-tex">\(\alpha\)</span> = 5 and <span class="math-tex">\(\beta\)</span> = -8<br />
<span class="math-tex">\(\alpha+\beta\)</span> = 5 + (-8)<br />
= -3<br />
<span class="math-tex">\(\alpha \beta\)</span> = 5 <span class="math-tex">\(\times\)</span> (-8)<br />
= -40<br />
For quadratic polynomials,<br />
p(x) = k(x<sup>2</sup> - (<span class="math-tex">\(\alpha\)</span>+<span class="math-tex">\(\beta\)</span>)x + <span class="math-tex">\(\alpha \beta\)</span>)<br />
= k(x<sup>2</sup> - (-3)x + (-40))<br />
= k(x<sup>2</sup> + 3x - 40)<br />
for k =1,<br />
p(x) = x<sup>2</sup> + 3x - 40</p>
Correct Answer: C