What kind of solutions does m^2 + m + 1 = 0 have?

2 Answers
Alan P.
Jul 8, 2015

m^2+m+1 = 0
has two imaginary solutions

Explanation:

If expressed in a standard quadratic form
color(white)("XXXX")am^2+bm+c=0

The discriminant Delta = b^2-4ac
indicates the number of roots
Delta ={(>0 rArr "2 Real roots"),(=0 rArr "1 Real root"), (<0 rArr "2 Imaginary roots"):}

b^2 - 4ac = 1^2 - 4(1)(1) = -3 <0

Meave60
Jul 8, 2015

The solutions include an imaginary number, sqrt(-3)=sqrt 3i.

Explanation:

m^2+m+1=0 is in the form of a quadratic equation ax^2+bx+c=0, where a=1, b=1, c=1.

Use the quadratic formula.

x=(-b+-sqrt(b^2-4ac))/(2a)

Substitute the values for a, b, and c into the quadratic formula.

x=(-1+-sqrt(1^2-4*1*1))/(2*1) =

x=(-1+-sqrt(1-4))/2 =

x=(-1+-sqrt(-3))/2

x=(-1+-sqrt3i)/2 =

x=(-1+sqrt3i)/2

x=(-1-sqrt3i)/2

x=(-1+sqrt3i)/2,(-1-sqrt3i)/2

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