Find the zeroes of the polynomial x2 + x - p(p + 1)
Answer: The zeroes of a polynomial are: p - 1 and p.
Let us proceed step by step
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