Find the zeroes of the polynomial x² + x - p(p + 1)

The zeroes of a polynomial are the values of x that make the entire value of the polynomial equal to 0.

Answer: The zeroes of a polynomial are: p - 1 and p.

Let us proceed step by step

Explanation: 

From the given polynomial x² + x - p(p + 1)

Step 1: Equating the given polynomial with 0

=> x² + x - p(p + 1) = 0

Step 2: Factorize the given polynomial and get the required factors.

After factorizing the given polynomial, we get

x²+ (p + 1)x - px - p(p + 1) = 0

Step 3: Taking x as common in ist two terms and -p as common in last two terms, we get

x(x + p + 1) -p(x + p + 1) = 0

Step 4: This can be further simplified as below

(x + p + 1) (x - p) = 0

On equating both the factors separately to 0, we get

x = - p - 1, and x = p

Thus the zeroes of a polynomial are p - 1 and p.