Question

Find the zeroes of the quadratic polynomials 3x² – x – 4 and verify the relationship between the zeroes and the coefficients.

Answer 1

Let f(x) = 3x² – x – 4

By splitting the middle term, we get

f(x) = 3x² – (4 – 3)x – 4 [∵ – 1 = 3 – 4 and 4×3 = 12]

= 3x² + 3x – 4x – 4

= 3x(x + 1) – 4(x + 1)

= (3x – 4) (x + 1)

On putting f(x) = 0, we get

(3x – 4) (x + 1) = 0

⇒ 3x – 4 = 0 or x + 1 = 0

x = 4/3 or x = – 1

Thus, the zeroes of the given polynomial 3x² – x – 4 are – 1 and 4/3.

Verification

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