How to obtain a quadratic equation, with integer coefficient, having roots 2+i√5 and 2-i√5 ?

1 Answer
Aug 30, 2017

#y=x^2-4x+9#

Explanation:

#"given the roots of a polynomial say "x=a" and "x=b#

#"then the factors of the polynomial are " #

#(x-a)" and " (x-b)#

#"the polynomial is then the product of the factors"#

#p(x)=(x-a)(x-b)#

#"here the roots are "x=2+isqrt5" and "x=2-isqrt5#

#rArr"factors are "(x-2+isqrt5)" and "(x-2-isqrt5)#

#rArry=((x-2)+isqrt5)((x-2)-isqrt5)#

#color(white)(rArry)=(x-2)^2-5i^2#

#color(white)(rArry)=x^2-4x+4+5#

#color(white)(rArry)=x^2-4x+9#