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

Answer:

$Sum = 1.67$

Step-by-step 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:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

Where:

$a = 1.5$

$b = -2.5$

$c = -1.5$

So, we have:

$x = \frac{-(-2.5)\±\sqrt{(-2.5)^2 - 4*1.5*-1.5}}{2*1.5}$

$x = \frac{2.5\±\sqrt{6.25 +9}}{3}$

$x = \frac{2.5\±\sqrt{15.25}}{3}$

$x = \frac{2.5\±3.91}{3}$

$x = \frac{2.5+3.91}{3}$ or $x = \frac{2.5-3.91}{3}$

The sum of the solution is then calculated as:

$Sum = \frac{2.5+3.91}{3} + \frac{2.5-3.91}{3}$

Take L.C.M

$Sum = \frac{2.5+3.91+2.5-3.91}{3}$

$Sum = \frac{5}{3}$

$Sum = 1.67$