Let f(x) = 2x2 – 8x + 6
By splitting the middle term, we get
f(x) = 2 x2 – (2 + 6)x + 6 [∵ – 8 = – (2 + 6) and 2×6 = 12]
= 2 x2 – 2x – 6x + 6
= 2x(x – 1) – 6(x – 1)
= (2x – 6) (x – 1)
On putting f(x) = 0, we get
(2x – 6) (x – 1) = 0
⇒2x – 6 = 0 or x – 1 = 0
⇒x = 3 or x = 1
Thus, the zeroes of the given polynomial 2 x2 – 8x + 6 are 1 and 3
Verification
So, the relationship between the zeroes and the coefficients is verified.