show by calculation, that the exact roots of the quadratic equation X^2+2x-5=0 are -1+_√6
Non
Coefficients are:
a = 1 , b = 2 , c = - 5
Discriminant:
D = b^2 - 4 a c
D = 2^2 - 4 • 1 • ( - 5 ) = 4 + 20 = 24
x1/2 = ( - b ± √D ) / 2 a
x1/2 = ( - 2 ± √24 ) / 2 • 1
x1/2 = ( - 2 ± √4•6 ) / 2
x1/2 = ( - 2 ± √4 • √6 ) / 2
x1/2 = ( - 2 ± 2 • √6 ) / 2
x1/2 = 2 • ( - 1 ± √6 ) / 2
x1/2 = - 1 ± √6