In a high-pressure experimental chamber, the relationship between Temperature, TTT, and Pressure, PPP, is modeled by the implicit equation:
T2−10T=2P2−16P+5 T^2 - 10T = 2P^2 - 16P + 5 T2−10T=2P2−16P+5Find an expression for dTdP\frac{dT}{dP}dPdT in terms of TTT and PPP.
The model predicts that temperature TTT has no real solutions for pressure values in the interval (p,q)(p, q)(p,q). Use your result from part (a) or otherwise to determine the value of ppp and the value of qqq.