Question

Question based on Nature of roots

Answer 1

If 2+i\[2+ i \sqrt{3}\] is a root of the equation x^2 + px + q = 0
where p ,q (belong to) rational numbers , then find the ordered pair (p,q)

Answer 2

\[\huge 2 + i \sqrt{3}\] is the root

Answer 3

then find p,q ?

Answer 4

yes

Answer 5

you know that if there is some complex root then the conjugate is also a root. So since this is a quadratic equation and you know one complex root, the missing one will be it's conjugate. Then use that p=-(1ºroot+2ºroot) and q=(1ºroot)(2ºroot)

Answer 6

thank you

Answer 7

yw