The pressure, $P$ , in a chemical reactor at time $τ\tau$ is modeled by the function

P(\tau) = 4\tau^3 - 10\tau^2 + 10\tau + \lambda, \quad \tau \ge 0

where $λ\lambda$ is a constant.

It is observed that the pressure reaches a zero-state when $τ=0.5\tau = 0.5$ , suggesting that $(2τ−1)(2\tau - 1)$ is a factor of $P(τ)P(\tau)$ .

Use the factor theorem to show that $λ=−3\lambda = -3$ .

Show that $P(τ)=0P(\tau) = 0$ has no other real solutions for $τ\tau$ .

The pressure, $P$ , in a chemical reactor at time $τ\tau$ is modeled by the function

P(\tau) = 4\tau^3 - 10\tau^2 + 10\tau + \lambda, \quad \tau \ge 0

where $λ\lambda$ is a constant.

It is observed that the pressure reaches a zero-state when $τ=0.5\tau = 0.5$ , suggesting that $(2τ−1)(2\tau - 1)$ is a factor of $P(τ)P(\tau)$ .

Use the factor theorem to show that $λ=−3\lambda = -3$ .

Show that $P(τ)=0P(\tau) = 0$ has no other real solutions for $τ\tau$ .

1.1 Algebra and functions

1.1 Algebra and functions Questions