Question

How do you solve `2x² - 7x + 15 = 0`?

Answer 1

Note that this equation has no Real roots. Complex roots can be determined using the quadratic formula.
`color(white)("XXXX")` `x= (7+sqrt(71)i)/4` or `x=(7-sqrt(71)i)/4`

Explanation:

The roots of a quadratic of the form
`color(white)("XXXX")` `ax^2+bx+c=0`
can be determined using the quadratic formula:
`color(white)("XXXX")` `x=(-b+-sqrt(b^2-4ac))/(2a)`

In this case:
`color(white)("XXXX")` `x=(7+- sqrt((-7)^2-4(2)(15)))/(2(2))`

`color(white)("XXXX")` `x= (7+-sqrt(-71))/4`

`color(white)("XXXX")` `x= (7+sqrt(71)i)/4` or `x=(7-sqrt(71)i)/4`