Multiple choice

Find the quadratic equation with rational coefficients which has $5-2\sqrt 5$ as a root.

  1. $x^2-10x-5=0$
  2. $x^2+10x+5=0$
  3. $x^2-10x+5=0$

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 5 - 2*sqrt(5) is a root, the other root is 5 + 2*sqrt(5). Sum of roots = 10. Product of roots = 25 - 4*5 = 5. The equation is x^2 - (sum)x + (product) = 0, which is x^2 - 10x + 5 = 0.

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