Finding the Value of k Using Zero of a Polynomial
Video Explanation
Question
If one zero of the quadratic polynomial
\[ f(x) = x^2 + 3x + k \]
is \(2\), find the value of \(k\).
Options:
(a) 10 (b) -10 (c) 5 (d) -5
Solution
Step 1: Use the Zero Condition
If \(2\) is a zero of the polynomial, then
\[ f(2) = 0 \]
Step 2: Substitute \(x = 2\)
\[ (2)^2 + 3(2) + k = 0 \]
\[ 4 + 6 + k = 0 \]
\[ 10 + k = 0 \]
Step 3: Solve for \(k\)
\[ k = -10 \]
Conclusion
The value of \(k\) is:
\[ \boxed{-10} \]
Hence, the correct option is (b) -10.