Let be the statement '' and be the statement 'the line meets the parabola at two distinct points'. Which of the following is correct? (Here is a real number.)

Answer and explanation

Correct answer: C. is both a necessary and a sufficient condition for

  1. Step 1: Setting gives , with discriminant .
  2. Step 2: Two distinct intersections need , i.e. : the statements are equivalent.
Answer
is both a necessary and a sufficient condition for .
Why not the others: At the line is a tangent (one intersection), so both statements are false there.

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