Let be the statement '' and be the statement ''. Which of the following is correct? (Here is a real number.)

Answer and explanation

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

  1. Step 1: , which is negative exactly between its roots: for .
  2. Step 2: So the two statements are true for exactly the same values of : each implies the other.
Answer
is both a necessary and a sufficient condition for .
Why not the others: No value of satisfies only one of the statements, since the quadratic is negative exactly on .

Practise more Necessary and sufficient conditions.

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