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Question:The square of a negative number is decreased by 14. The resulting number is 5 times the original number. What is the reciprocal of the original number? A) 1/2 B) 1/4 C) 1/5 D) 1/7 Answer:A.
Let x be the negative number. So, (x)^2  14 (reduced by 14) = 5x (five times the orginal number, x) x^2  5x 14 = 0. Solve for the roots. x = [ b +/ sqrt(b^2  4ac)]/2a x = [5 +/ sqrt(25 + 56)]/2 x = (5 +/ sqrt(81))/2 x = (5 +/ 9)/2 x = 4/2 or x = 14/2 or, x = 2 or x = 7 Since we are talking negative numbers, x = 2 and the reciprocal is 1/2 Hence, the answer is 1/2.
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