##### can you show the complete detailed steps from p^2 + p-(Answered)

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**Question**

- can?you?show?the?complete detailed?steps?from?
- ?p^2 + ?p ?10?/3 = 0

?p = (-? +/- (?^2 - 4*1*10?/3))/(-2)?

to get?

P = (?^2 - 43?/3)/-2

And

P = (-?^2 - 37?/3)/-2

a) For equilibrium, it?s correct that dp/dt should be made equal to zero.

Now, we arrive at the following expression:

?p^2 + ?p ?10?/3 = 0

This can be solved for p but the answer would be in terms of ? as suggested by you.

So the answer would be given by using:

x=(-b +/- ((b^2-4ac)^0.5)/2a)

so p = (-? +/- (?^2 ? 4*1*10?/3))/(-2)

Now the solutions for p thus obtained are also quadratic in nature, thus the solutions are:

P = (?^2 ? 43?/3)/-2

And the other solution is :

P = (-?^2 ? 37?/3)/-2

b) The quadratic equation obtained for p above:

?p^2 + ?p ?10?/3 = 0

Now the determinant of this quadratic equation is:

D = ?^2 ? 40?/3

This equation will have 2 solutions if the value of D is more than 0, it will have 1 solution if the value of D is 0 and

it will have 0 that means no solution when the value of D is negative.

So, for 2 solutions the value of D = ?^2 ? 40?/3 >0

For 1 solution, value of D = ?^2 ? 40?/3 = 0

For 0 solution, value of ?^2 ? 40?/3 < 0.

Paper#9210098 | Written in 27-Jul-2016

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