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JAMB 1990 · UME · Q30

At what value of xx is the function x2+x+1x^2 + x + 1 a minimum?

Worked solution (try it first)
  1. Complete the square: half of 1 is 12\frac12, so x2+x+1=(x+12)2+34x^2 + x + 1 = \left(x + \frac12\right)^2 + \frac34.
  2. A square is least when it is zero, which happens when x+12=0x + \frac12 = 0.
  3. So the minimum is at x=−12x = -\frac12, option B.

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