Polynomials
Grade Class 10
Question:
<p>If one zero of the quadratic polynomial <span class="math-tex">\({x^2} + {\text{ }}3x{\text{ }} + {\text{ }}k\)</span> is 2, then the value of ‘k’ is</p>
<p style="display:inline">– 10</p>
<p style="display:inline">10</p>
<p style="display:inline">5</p>
<p style="display:inline">– 5</p>
Step-by-Step Solution
Key Concept: If a number is a zero of a polynomial, then substituting that value into the polynomial must result in an output of zero.
<p>Given Polynomial is <span class="math-tex">$ p(x)= x^2+3x+k$</span></p>
<p>According to question, <span class="math-tex">$p(x)=0$</span> (Put x = 2)</p>
<p> p(2) = 0</p>
<p><span class="math-tex">$ \Rightarrow $</span><span class="math-tex">${\left( 2 \right)^2} + 3 \times 2 + k = 0$</span></p>
<p> <span class="math-tex">$ \Rightarrow $</span><span class="math-tex">$4 + 6 + k = 0$</span></p>
<p><em><strong> <span class="math-tex">$ \Rightarrow $</span><span class="math-tex">$k = - 10$</span></strong></em></p>
Correct Answer: A