Question 857230
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 {{{ax^2 + bx + c = 0}}} where a ≠ 0.
The roots are {{{(-b +- sqrt(b^2-4ac))/2a}}} (Quadratic Formula)
The roots are real if the expression inside the square root is non-negative.
{{{x^2 -x +3 = k}}} can be expressed as {{{x^2 - x + (3 - k) = 0}}}
a = 1, b = -1 and c = 3 - k
so {{{b^2 - 4ac = (-1)^2 - 4(1)(3 - k) >= 0}}}
{{{4k - 11 >= 0 }}}
{{{highlight(k >= 11/4)}}}