The pressure, PPP, in a chemical reactor at time τ\tauτ is modeled by the function
P(τ)=4τ3−10τ2+10τ+λ,τ≥0 P(\tau) = 4\tau^3 - 10\tau^2 + 10\tau + \lambda, \quad \tau \ge 0 P(τ)=4τ3−10τ2+10τ+λ,τ≥0where λ\lambdaλ is a constant.
It is observed that the pressure reaches a zero-state when τ=0.5\tau = 0.5τ=0.5, suggesting that (2τ−1)(2\tau - 1)(2τ−1) is a factor of P(τ)P(\tau)P(τ).
Use the factor theorem to show that λ=−3\lambda = -3λ=−3.
Show that P(τ)=0P(\tau) = 0P(τ)=0 has no other real solutions for τ\tauτ.
