Question 224409
if 2x^2 - 14x + 29 = p(x+q)^2 +r holds for all real values of x, find the values of p,q and r. Hence, state the minimum value of the function and the corresponding value of x.. 
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2x^2 - 14x + 29 = px^2 + 2pqx +pq^2 +r
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Matching up the coefficients you get:
p = 2
2pq= -14
pq^2+r = 29
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So:
p = 2 
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q = (14/4) = 7/2
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2(7/2)^2+r = 29
(49/2) + r = (58/2)
r = 9/2
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Hence, state the minimum value of the function and the corresponding value of x
a = 2 ; b = -14
min occurs at x = -b/2a = 14/4 = 7/2
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2x^2 - 14x + 29 
Minimum value is 2(29)^2 - 14*29 +29 = 1305
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Cheers,
Stan H.
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