Vector Problem: Clarity on Part (f) & Why 2.15 Only

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The discussion centers on clarifying why the solution to part (f) of a vector problem only accepts the value t=2.15, despite both t=2.79 and t=2.15 satisfying part (e). The original poster is confused about which time value is considered first and seeks assistance specifically for part (f). Participants acknowledge the complexity of the problem and express gratitude for the help. Ultimately, the focus remains on understanding the reasoning behind the selection of t=2.15 as the correct answer.
chwala
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Homework Statement
kindly see attached problem
Relevant Equations
vectors
1619311735493.png

1619311779300.png
i need clarity on part (f) only...we have two values for ##t## i.e ## t=2.79## and ##t=2.15##, ...the mark scheme says solution is:

1619311920632.png


why ##2.15## only, i have tried substituting the two values back into the problem and they both satisfy part ##e##
 
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I need help on part ##f## only.
 
Which of the two time values that you got is first?
 
FactChecker said:
Which of the two time values that you got is first?
ok i see quite tricky...thanks mate. :cool:
 
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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