Question

Solve the following quadratic equation for x and give your answer correct to three significant figures: 2x² − 10x + 5 = 0

Answer 1

Given:

2x² − 10x + 5 = 0

Where:

a = 2

b = −10

c = 5

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

`x = (-(-10) +- sqrt((-10)^2-4(2)(5)))/(2(2))`

`= (10+- sqrt(100-40))/4`

`= (10+- sqrt60)/4`

`=sqrt60`

= 7.746

`x = (10+- 7.746)/4`

First root:

`x = (10+7.746)/4`

`=17.746/4`

= 4.4365

= 4.44​

Second root:

`x = (10-7.746)/4`

`= 2.254/4`

= 0.5635

= 0.564

x = 4.44 or x = 0.564​