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1956 AMC 12 Question 23

AMC12 · 1956 AMC 12

Question 23

About the equation $ax^2-2x\sqrt2+c=0,$ with $a$ and $c$ real constants, we are told that the discriminant is zero. The roots are necessarily:
  1. equal and integral
  2. equal and rational
  3. equal and real
  4. equal and irrational
  5. equal and imaginary