Question

Find the zeroes of the quadratic polynomials 3x² + 5x – 2 and verify the relationship between the zeroes and the coefficients.

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.