Question

for the polynomial x2-5x+6, find the sum of zeroes

Answer 1

 x2 – 5x + 6
                 = x2 – 3x – 2x + 6
                 = x(x – 3) – 2(x – 3)
                 = (x – 3)(x – 2)
∴ (x – 3)(x – 2) = 0
⇒ x – 3 = 0 or x – 2 = 0
⇒ x = 3 or x  = 2
Thus 3 and 2 are the zeroes of the given polynomial
Sum of roots (α+ β) = (3+2) = 5 = − (−5/1) = − (b/a)
Product of roots (αβ) = 3 × 2 = 6 = (6/1)  = (c/a)