Let the reciprocals of the roots of x^2 - 2x + 5 = 0 be a and b. Evaluate a*b.
+23246 x2 - 2x + 5 = 0
Using the quadratic formula:
x1 = [ 2 + sqrt( (-2)2 - 4(1)(5) ) ] / [ (2)(1) ] = [ 2 + sqrt( 4 - 20) ] / 2 = [ 2 + sqrt(-16) ] / 2 = ( 2 + 4i ) / 2 = 1 + 2i
x2 = [ 2 - sqrt( (-2)2 - 4(1)(5) ) ] / [ (2)(1) ] = [ 2 - sqrt( 4 - 20) ] / 2 = [ 2 - sqrt(-16) ] / 2 = ( 2 - 4i ) / 2 = 1 - 2i
a = 1 / ( 1 + 2i )
b = 1 / ( 1 - 2i )
a·b = [ 1 / ( 1 + 2i ) ] · [ 1 / ( 1 - 2i ) ] = 1 / ( 12 - (2i)2 ) = 1 / ( 1 + 4 ) = 1 / 5
