Question

Let `p, q in R` . If ` 2- sqrt3` is a root of the quadratic equation, `x^(2)+px+q=0,` then (A) `q^(2)-4p-16=0` (B) `p^(2)-4q-12=0` (C) `p^(2)-4q+12=0` (D) `q^(2)-4p+14=0`
A. `q^(2)-4p-16=0`
B. `p^(2)-4q-12=0`
C. `p^(2)-4q+12=0`
D. `q^(2)-4p+14=0`

Answer 1

Correct Answer - B
Given quadratic equation is `x^(2)+px +q=0,` where `p, q in R` having one root `2-sqrt3,` then other root is `2+sqrt3` (conjugate of `2-sqrt3)[because` irratinal rootal of a quadratic equation alwayss occurs in pairs]
So, sum of roots `=-p4impliesp=-4`
and product of roots `=q=4-3impliesq=1`
Now, from options `p^(20-4q-12=16-4-12=0`