Polynomials
Grade Class 10
Question:
<p>If one of the zeroes of the quadratic polynomial (k – 1) x<sup>2</sup> + kx + 1 is –3, then the value of k is</p>
<p style="display:inline"><span class="math-tex">\(\frac{-2}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{2}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{-4}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{4}{3}\)</span></p>
Step-by-Step Solution
Key Concept: A value is a zero of a polynomial if and only if substituting it into the polynomial for x results in an expression equal to zero.
<p>Zeroes of a polynomial are the values of x at which the polynomial is equal to zero.<br />
As one of the zeros of given polynomial p(x) = (k - 1) x<sup>2</sup> + kx + 1 is -3, Therefore<br />
p (- 3) = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> (k - 1)(- 3)<sup>2</sup> + k(- 3) + 1 = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> (k - 1)(9) - 3k + 1 = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> 9k - 9 - 3k + 1 = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> 9k - 3k - 8 = 0<br />
<span class="math-tex">\(\Rightarrow\)</span> 6k = 8<br />
<span class="math-tex">\(\Rightarrow\)</span> k = 4/3</p>
Correct Answer: D