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

Answer 1

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

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#
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Answer 2

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

#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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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