2002 AMC 10A Problem 14 — Solution | LIVE by Po-Shen Loh

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2002 AMC 10A Problem 14

Attempt Problem 14 of the 2002 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

14.

Both roots of the quadratic equation $x^2-63x+k=0$ are prime numbers. The number of possible values of $k$ is

$0$

$1$

$2$

$4$

more than four

Answer: B

Concepts:Vieta’s Formulas prime parity

Difficulty rating: 1310

Solution:

If the roots are primes $p$ and $q,$ then $p+q=63$ and $pq=k.$ Because $63$ is odd, one prime must be $2,$ making the other $61,$ which is prime.

So $k=2\cdot 61=122$ is the only possible value.

Thus, the correct answer is B.

← Problem 13#13

Problem 15#15 →

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