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Let p, q in R . If 2- sqrt3 is a root ...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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