1952 AMC 12 Problem 6

Attempt Problem 6 of the 1952 AMC 12 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 1952 AMC 12 solutions, or check the answer key.

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

6.

The difference of the roots of x2−7x−9=0x^2-7x-9=0 is:
+7+7
+72+\dfrac72
+9+9
2852\sqrt{85}
85\sqrt{85}
Answer: E
Concepts:quadratic
Small hint:
Write the two roots using the quadratic formula
Big hint:
Their separation is the square root of the discriminant because the leading coefficient is 11
Solution:
The roots are 7+49+362\dfrac{7+\sqrt{49+36}}2 and 7−49+362.\dfrac{7-\sqrt{49+36}}2. Their positive difference is therefore 85.\sqrt{85}.
Thus, the correct answer is E.
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