16Hit1600
Advanced MathVery hardDiscriminant and number of real solutions

Advanced Math practice question

For which value of c does the equation x² + 6x + c = 0 have exactly one real solution?

  1. A. 9Correct
  2. B. 6
  3. C. −9
  4. D. 3

Answer: A. 9

One real solution means discriminant 0: 36 − 4c = 0, so c = 9. (Then (x + 3)² = 0.)

Why the other answers are wrong

B. 6
c = 6 gives discriminant 36 − 24 = 12 > 0: two solutions.
C. −9
c = −9 gives 36 + 36 = 72 > 0: two solutions.
D. 3
c = 3 gives 36 − 12 = 24 > 0: two solutions.

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