Question

find the zeros of a quadratic polynomial given 3x²-x-4 and alsl verify the relationship between the zeroes and coefficient ​

Answer 1

Step-by-step explanation:

First ,

Factorise the polynomial 3x^2 - x - 4

By splitting the middle term,

3x^2 - 4x + 3x - 4

x (3x - 4) + 1 (3x -4)

(3x - 4) (x + 1)

3x - 4 = 0 x + 1 = 0

3x = 4 x = -1

x = 3/4

3/4 and -1 are the only two zeroes of p(x).

Hope it will help you

Answer 2

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.(in attachment)