Question

If one zero of the polynomial \(x^2 - 5x - c\) is (-1), find the value of c. Also, find the other zero.

Hint:

For polynomial \(x^2 + bx + c\), the sum of zeroes is \(-b\) and the product is \(c\). This shortcut only works when the coefficient of \(x^2\) is 1.

Answer 1

Step 1: Solving OR (B):
1. If \(-1\) is a zero, \(p(-1) = 0\):
\[ (-1)^2 - 5(-1) - c = 0 \implies 1 + 5 - c = 0 \implies c = 6 \] 2. The polynomial is \(x^2 - 5x - 6\).
3. Let the other zero be \(\beta\). Sum of zeroes: \(-1 + \beta = -(-5)/1 = 5\).
4. \(\beta = 5 + 1 = 6\).
Step 2: Final Answer (OR):
The value of \(c\) is 6, and the other zero is 6.