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Popular >

x^2-x+1>= 0

Solution

x^{2} - x + 1 \geq 0

Solution

True for all x

+1

Interval Notation

(- \infty, \infty)

Solution steps

x^{2} - x + 1 \geq 0

Complete the square

x^{2} - x + 1 : (x - \frac{1}{2})^{2} + \frac{3}{4}

(x - \frac{1}{2})^{2} + \frac{3}{4} \geq 0

Move

\frac{3}{4}

to the right side

(x - \frac{1}{2})^{2} \geq - \frac{3}{4}

If n is even,

u^{n} \geq 0

for all

u

True for all x

Popular Examples

\frac{3}{2 x - 1} < - 2

x (x - 10) < - 2 x - 7

((x+3))/((x+1))<5

\frac{( x + 3 )}{( x + 1 )} < 5

x*(x+2)^2*(x-1)^5*(2x-3)*(x-3)^4>= 0

x \cdot (x + 2)^{2} \cdot (x - 1)^{5} \cdot (2 x - 3) \cdot (x - 3)^{4} \geq 0

((x^2-2x)(2x-2)-9*(2x-2))/((x^2-2x))<= 0

\frac{( x ^{2} - 2 x ) ( 2 x - 2 ) - 9 \cdot ( 2 x - 2 )}{( x ^{2} - 2 x )} \leq 0

Frequently Asked Questions (FAQ)

What is x^2-x+1>= 0 ?
The solution to x^2-x+1>= 0 is True for all x