How do you solve #x^2+3>2x# using a sign chart?

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Answer 1 · 2017-02-27T10:05:05

The solution is # x in RR#

Let's rewrite the equation

#x^2-2x+3>0#

Let #f(x)=x^2-2x+3#

We need the roots of

#x^2-2x+3=0#

Let's calculate the discriminant

#Delta=b^2-4ac=(-2)^2-4(3)(1)#

#=4-12=-8#

As, #Delta<0#, there are no real roots

So,

#AA x in RR#, #f(x)>0#

graph{x^2-2x+3 [-6.176, 6.31, -0.31, 5.93]}