An algebra problem by A Former Brilliant Member

Algebra Level 5

$\large x^2+ax+b=0$

Consider the above equation :

Following conversation follows between three friends regarding the equation:

A : If $m+in$ is a solution to the equation , then $m-in$ is necessarily a solution to the equation where $n \neq 0$

B : The given equation can have a real and an imaginary root.

C : The given equation can either have two real or two imaginary roots but cannot have one real and one imaginary root.

Who is correct?

Details and Assumptions :

$i=\sqrt{-1}$
$a$ and $b$ can be complex or real numbers.

A B C A & C

2 solutions

Kushal Dey
Dec 2, 2020

From A and C are saying, it is implied that the coefficients of the quadratic equation are always real which may or may not be true, whereas B is saying that maybe 1 root is real and other is imaginary which "may-be" true. This question just involves understanding the language of the problem.

A Former Brilliant Member
Jan 10, 2018

Consider the given equation:

$x^2+(i+1)x+i=0$

Roots of the above equation are $-1,-i$

This doesn't really proof whether the other statements are true or false.

Peter van der Linden - 3 years, 5 months ago

C : The equation cannot have one real and one imaginary root which is proved false by given example.

A is also proved false as $0-i$ is a solution to the given equation but $0+i$ is not a solution to the given equation.

A Former Brilliant Member - 3 years, 5 months ago

An algebra problem by A Former Brilliant Member

2 solutions

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