Question

C-1 If ` 2+ isqrt3` is a root of the equation `x^2 + px + q = 0`, Where p,q `in` R, then find the ordered pair ( p,q).

Answer 1

Here, one root is given that is `2+isqrt3`.
So, the second root will be `2-isqrt3`.
Given equation is,`x^2+px+q = 0`.
So, sum of roots,
`-p/1 = 4=> p = -4`
Product of roots,
`q/1 = (2+isqrt3)(2-isqrt3)=> q = 2^2+sqrt3^2 => q = 7`
So, ordered pair `(p,q)` will be `(-4,7)`.