Question

Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2

Answer 1

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

Answer 2

Answer:

The polynomial is   $-1y^{2}+8y-16$

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 $y^{2}$ 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.

       $-1y^{2}+8y-16$

For sol        $-1y^{2}+8y-16=0$

                   $(y-4)^{2}=0$

This implies the above polynomial is of multiplicity 2