Question

Hi can anyone help me with this question without the use of calculators please?

Answer 1

`(11)/(6)` units

Explanation:

To find the x- intercepts let y = 0 , that is

6x² - 7x - 3 = 0 ← in standard form

(3x + 1)(2x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = -
`(1)/(3)`

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

Find the difference of the 2 x- intercepts using absolute value

distance = |
`(3)/(2)` - (-
`(1)/(3)` ) | = |
`(3)/(2)` +
`(1)/(3)` | = |
`(11)/(6)` | =
`(11)/(6)`