Question
Solve the given two equations and answer the two
questions that follow as per the instructions given below. I. (1/4) + 7.5p(-2) = 3.625p (-1) II. 0.5q2 - 3.25q = 6Â Suppose the smaller root of equation 'II' and the greater root of equation 'I' are utilized to construct a new equation 'III' in terms of the variable 'r', which of the following represents equation 'III'?Solution
ATQ, Equation I, 1/4 + 7.5p(-2) = 3.625p(-1) 7.5/p2- 3.625/p + 1/4 = 0 30 - 14.5p + p2 = 0 (p - 2.5)(p - 12) = 0 p = 2.5, 12 Equation II, 0.5q2- 3.25q = 6 q2 - 6.5q - 12 = 0 (q + 1.5)(q - 8) = 0 q = - 1.5, 8 Roots of Equation III =( - 1.5, 12 ) Equation III, (r + 1.5)(r - 12) = 0 r2 - 10.5z - 18 = 0 2r2Â - 21r = 36
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