Respuesta :

[tex]\bf \stackrel{\textit{root of 4}}{x=4\implies x-4=0}\qquad \stackrel{\stackrel{multiplicity}{of~two}}{(x-4)^2}\qquad \implies \stackrel{FOIL}{x^2-8x+16} \\\\\\ \stackrel{\textit{multiplying by -1}}{-1x^2+8x-16}[/tex]

Answer:

The polynomial is   [tex]-1y^{2}+8y-16[/tex]

Step-by-step explanation:

we have to construct a second degree polynomial function has a leading coefficient of -1 that means polynomial having the highest power 2  and having the coefficient of [tex]y^{2}[/tex] is -1.

One more condition is that having the root 4 with multiplicity 2

Multiplicity means how many times a particular root get when equate to zero or we can say a number is zero for given polynomial function.

       [tex]-1y^{2}+8y-16[/tex]

For sol        [tex]-1y^{2}+8y-16=0[/tex]

                   [tex](y-4)^{2}=0[/tex]

This implies the above polynomial is of multiplicity 2

 

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