How do you solve #2x² - 7x + 15 = 0#?

1 Answer
Alan P.
Jun 26, 2015

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#

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