Let $p(x)=816x^3-3835x^2+6000x-3125.$

a$.$ Find all exact roots of $p.($Hint: $p$ is divisible by $(3x-5)).$

b$.$ Plot $p$ with Python in the interval $1\mathrm{.}43,1\mathrm{.}71.($Hint: you can use $x=$ linspace $(1\mathrm{.}43,1\mathrm{.}71)$

together with the plot function$).$

c$.$ What do you get via Newton's method with $x_0=1\mathrm{.}5?($Hint: replace the function and the

initial point in our Newton code$).$

d$.$ What do you get via the secant method with $x_0=1$ and $x_1=2?($Hint: replace the

function and the initial points in our secant code$).$

e$.$ What do you get via the bisection method applied to the interval $[1,2]?($Hint: replace the

function and the interval endpoints in our bisection code$)$