<p>The zeroes of the polynomial p(x) = 25x<sup>2</sup> - 49 are:</p>
<p style="display:inline"><span class="math-tex">\(\frac{7}{5}\)</span>, <span class="math-tex">\(-\frac{7}{5}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{7}{5}\)</span>, <span class="math-tex">\(\frac{7}{5}\)</span></p>
<p style="display:inline"><span class="math-tex">\(-\frac{49}{25}\)</span>, <span class="math-tex">\(+\frac{49}{25}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac {49}{25}\)</span>, <span class="math-tex">\(\frac {49}{25}\)</span></p>
Step-by-Step Solution
Key Concept: To find the zeros of a binomial in the form ax^2 - b, factor it using the difference of squares identity a^2 - b^2 = (a - b)(a + b) and set each factor to zero.
<p>p(x) = 25x<sup>2</sup> - 49 = 0<br />
= (5x - 7)(5x + 7) = 0<br />
<span class="math-tex">$\therefore$</span> x = <span class="math-tex">$\frac{7}{5}$</span> and <span class="math-tex">$\frac{-7}{5}$</span></p>
Correct Answer: A