Use the MATLAB roots function to find all the roots of the following polynomialFor fluid flow in pipes, friction is described by a dimensionless number, the Fanning

friction factor $f.$ The Fanning friction factor is dependent on a number of parameters

related to the size of the pipe and the fluid, which can all be represented by another

dimensionless quantity, the Reynolds number Re$.$ A formula that predicts $f$ given $Re$ is

the von Karman equation:

$f^{-0\mathrm{.}5}=4lo{g}_{10}(Re{f}^{0\mathrm{.}5})-0\mathrm{.}4$

Typical values for the Reynolds number for turbulent flow are $10,000$ to $500,000$ and for

the Fanning friction factor are $0\mathrm{.}001$ to $0\mathrm{.}01.$ Develop a function that uses the fzero

function to compute $f$ given a user$-$supplied value of Re between $2500$ and $250,000.$

Report values $f$ for $5$ values of Re$.$

functions:

$($a$)f(x)=0\mathrm{.}007x^4-0\mathrm{.}284x^3+3\mathrm{.}355x^2-12\mathrm{.}183x+5$

$($b$)f(x)=x^5-16\mathrm{.}05x^4+88\mathrm{.}75x^3-192\mathrm{.}0375x^2+116\mathrm{.}35x+31\mathrm{.}6875$