Let f(x) = 10x2 + 3x – 1
By splitting the middle term, we get
f(x) = 10x2 – 2x + 5x – 1
= 2x(5x – 1) + 1(5x – 1)
= (2x + 1) (5x – 1)
On putting f(x) = 0, we get
(2x + 1) (5x – 1) = 0
⇒ 2x + 1 = 0 or 5x – 1 = 0
x = -1/2 or x = 1/5
Thus, the zeroes of the given polynomial10x2 + 3x – 1 are -1/2 and 1/5.
Verification
So, the relationship between the zeroes and the coefficients is verified.