Question

What is the sum of the solutions of the equation 1.5x^2 - 2.5x -1.5 = 0? Round to the nearest hundredth. ​

Answer 1

`Sum = 1.67`

Explanation:

Given:

`1.5x^2 - 2.5x -1.5 = 0`

Required

Determine the sum of the solutions

This question will be answered using quadratic formula:

`x = (-b\±√(b^2 - 4ac))/(2a)`

Where:

`a = 1.5`

`b = -2.5`

`c = -1.5`

So, we have:

`x = (-(-2.5)\±√((-2.5)^2 - 4*1.5*-1.5))/(2*1.5)`

`x = (2.5\±√(6.25 +9))/(3)`

`x = (2.5\±√(15.25))/(3)`

`x = (2.5\±3.91)/(3)`

`x = (2.5+3.91)/(3)` or
`x = (2.5-3.91)/(3)`

The sum of the solution is then calculated as:

`Sum = (2.5+3.91)/(3) + (2.5-3.91)/(3)`

Take L.C.M

`Sum = (2.5+3.91+2.5-3.91)/(3)`

`Sum = (5)/(3)`

`Sum = 1.67`