Question

find the zeros of the following polynomials 3x²+5x-2​

Answer 1

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 and 1/3.

Verification So, the relationship between the zeroes and the coefficients is verified

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