Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the cofficients.1. 3x^2-x-4​

Answer 1

Given :-

$\sf 3x^{2} -x-4$

To Find :-

Zeroes and verify

Solution :-

3x² - (3x - 4x)  - 4 = 0

3x² - 3x + 4x - 4 = 0

3x(x + 1) - 4(x + 1) = 0

(3x - 4)(x + 1) = 0

Either

3x - 4 = 0

3x = 0 + 4

3x = 4

x = 4/3

or

x + 1 = 0

x = 0 - 1

x = -1

Verification

4/3 + (-1) = -(-1)/3

4/3 - 1 = 1/3

4 - 3/3 = 1/3

1/3 = 1/3

And

4/3 × -1 = -4/3

-4/3 = -4/3

Answer 2

Given :-

$\sf 3x^{2} -x-43x$

To Find :-

Zeroes and verify

Solution :-

3x² - (3x - 4x) - 4 = 0

3x² - 3x + 4x - 4 = 0

3x(x + 1) - 4(x + 1) = 0

(3x - 4)(x + 1) = 0

Either

3x - 4 = 0

3x = 0 + 4

3x = 4

x = 4/3

or

x + 1 = 0

x = 0 - 1

x = -1

Verification

4/3 + (-1) = -(-1)/3

4/3 - 1 = 1/3

4 - 3/3 = 1/3

1/3 = 1/3

And

4/3 × -1 = -4/3

-4/3 = -4/3