Multiple choice

Find c, if the quadratic equation $x^{2}\, -\, 2\, (c\, +\, 1)\, x\, +\, c^{2}\, =\, 0 $ has real and equal roots.

  1. $c=\cfrac{1}{2}$
  2. $c=-\cfrac{1}{2}$
  3. $c=2$
  4. $c=-2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For real and equal roots, the discriminant b^2 - 4ac = 0. Here, [-2(c+1)]^2 - 4(1)(c^2) = 0. 4(c^2 + 2c + 1) - 4c^2 = 0. 4c^2 + 8c + 4 - 4c^2 = 0. 8c + 4 = 0, so c = -1/2.

AI explanation

For equal roots, the discriminant must be zero, so using the formula D equals b squared minus 4ac, we set [-2(c + 1)] squared minus 4 times 1 times c squared equal to 0. Expanding this yields 4 times the quantity c squared plus 2c plus 1, minus 4c squared, equals 0. Simplifying gives 8c plus 4 equals 0, which means c equals negative one half.

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