Question

Find the zeroes of the polynomial `x^2 + x – p(p + 1) ` 

 

Answer 1

f(x) = x2 + x – p (p + 1)
By adding and subtracting px, we get
`f(x) = x^2 + px + x – px – p(p + 1)`
= `x^2 + (p + 1) x – px –p (p + 1)`
=` x[x + (p + 1)] –p [x + (p + 1)]`
= `[x + (p + 1)] (x – p)`
`f(x) = 0`
⇒`[x + (p + 1)] (x – p) = 0`
⇒ `[x + (p + 1)] = 0 or (x – p) = 0`
⇒ `x = – (p + 1) or x = p`
So, the zeroes of f(x) are – (p + 1) and p.