Let p,q R. · questionr

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Joint Entrance Examination
Mathematics
Complex Numbers
Question 287

Question 287 of 455MediumMCQ

Let

p,q\in\mathbb R

. If

2-\sqrt{3}

is a root of

x^2+px+q=0

, then:

A

p^2-4q+12=0

B

q^2-4p-16=0

C

q^2+4p+14=0

D

p^2-4q-12=0

Press A-D to select · Enter to check

Solutions · 1

Official solution

The conjugate surd root

2+\sqrt{3}

must also be a root:

x^2+px+q=(x-2+\sqrt{3})(x-2-\sqrt{3})=x^2-4x+1

. So

p=-4,\ q=1

, and

p^2-4q-12=16-4-12=0.

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