Find the product of the zeroes of the quadratic polynomial 3x 2 +5x +2
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Sol.
Let f(x) = 3x2 + 5x – 2
By splitting the middle term, we get
f(x) = 3x2 + (6 – 1)x – 2 [∵ 5 = 6 – 1 and 2×3 = 6]
= 3x2 + 6x – x – 2
= 3x(x + 2) – 1(x + 2)
= (3x – 1) (x + 2)
On putting f(x) = 0 , we get
(3x – 1) (x + 2) = 0
⇒ 3x – 1 = 0 or x + 2 = 0
x = 1/3 or x = – 2
Thus, the zeroes of the given polynomial 3x2 + 5x – 2 are – 2 and1/3
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