How do you describe the roots of #4x^2 - 3x + 2 = 0#?

1 Answer
George C.
Jan 30, 2016

A conjugate pair of Complex roots.

Explanation:

#4x^2-3x+2# is of the form #ax^2+bx+c# with #a=4#, #b=-3# and #c=2#.

This has discriminant #Delta# given by the formula:

#Delta = b^2-4ac = (-3)^2-(4*4*2) = 9-32 = -23#

Since #Delta# is negative, the quadratic equation has no Real roots. It has a pair of Complex roots, conjugate to one another, given by the quadratic formula:

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

#=(-b+-sqrt(Delta))/(2a)#

#=(3+-sqrt(-23))/(2*4)#

#=3/8+-sqrt(23)/8i#

where #i# is the imaginary unit.

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