SOLUTION: If the quadratic equation x^2 -x +3 = k has real roots, find the range of values of k. The answer is k is greater than or equal to 11/4. And what I get is k = 11/4. I don't unde

Question 857230: If the quadratic equation x^2 -x +3 = k has real roots, find the range of values of k.
The answer is k is greater than or equal to 11/4. And what I get is k = 11/4. I don't understand why greater than or equal to is used instead of equal to. Thanks for your help.
Found 2 solutions by josgarithmetic, reviewermath:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Maybe the wording has thrown your concept off? Maybe you forgot that the question was about "range", and you momentarily mistook at as something else?

The wording, the quadratic equation x^2 -x +3 = k has real roots, is like f(x)=x^2-x+3, and then renaming f(x) as k.
NOW, what is the range for f(x)? That is all the question asks.

Note that your function based on qualitative familiarity with this type of function, has a minimum and is concave upward. The vertex is a MINIMUM; all values of the function are GREATER THAN OR EQUAL to the minimum value, which you found as 11/4.
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
Q:
If the quadratic equation x^2 -x +3 = k has real roots, find the range of values of k.
The answer is k is greater than or equal to 11/4. And what I get is k = 11/4. I don't understand why greater than or equal to is used instead of equal to
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A:
In where a ≠ 0.
The roots are (Quadratic Formula)
The roots are real if the expression inside the square root is non-negative.
can be expressed as
a = 1, b = -1 and c = 3 - k
so

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