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x^2 + x +1 is always Options are -A)positive B)negative C)0 D)constant Give reasons .

x^2 + x +1 is always Options are -A)positive B)negative C)0 D)constant Give reasons .

Grade:11

5 Answers

Arun
25750 Points
6 years ago
this will be always positive.
because here after comparing from ax^2+ bx+ c = 0
Discriminant is negative and a is positive hence it will be positive always
Note- if Discriminant is negative and a is also negative then this equation is always negative.
and also it can be written as
(x+ 1/2)2 + 3/4
as we know square of any number is positive always or zero and further we are adding 3/4 too.
hence it will be positive always.
hope it helps
shailesh suran
19 Points
6 years ago
this will always be positive 
as the value of the expresion belongs to [4ac-b2/4a ,∞)
where a=1 ,b=1 ,c=1
by substituting the values of a,b and c we get[3/4,∞)
as the value of the expression can never be less than ¾  
 it  is always positive
 
manoj kumar
30 Points
6 years ago
Always positive BecauseWe can modify equation in this form (x+1/2)^2 +3/4 in this (x+1/2)^2 is always positive So answer is positive
Shailendra Kumar Sharma
188 Points
6 years ago
let x2+x+1 be the function
Now x2+x+1/4 +3/4
(x+1/2)^2+3/4 
sine (x+1/2)^2 will always be greater than or equal to zero the minimum value of this function is ¾ so it will always be positive
other way to look at is D0 so all the function will be above X axis so no negetive y values
Venky
21 Points
6 years ago
Answer is positiveBecause for any real numbers x^2+x+1 is positive Ex: if x=1 then x^2+x+1.is 3 (positive) similarly for all x belongs to positive real numbers then answer is positiveIf x=-1 then x^2+x+1 is 1 (positive) similarly for all x=negative real numbers ans is positive If x=0 then x^2+x+1=1 (positive)

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