Explanation:
The roots of the qunitic polynomial is given below as
[tex]\begin{gathered} x_1=-4(order2) \\ x_2=5(order3) \\ y-intercept=52 \end{gathered}[/tex]
The general form of a plolynomial is given below as
[tex]y=a(x-n)(x-m)(x-p)[/tex]
In this case,
the equation will be given below as
[tex]y=a(x+4)^2(x-5)^3[/tex]
To apply the intercepts, we will use the coordinates below to find the value of a
[tex](0,52)[/tex][tex]\begin{gathered} y=a(x+4)^{2}(x-5)^{3} \\ 52=a(4^2)(-5)^3 \\ 52=-2000a \\ divide\text{ both sides by -2000} \\ a=-\frac{52}{2000} \\ a= \end{gathered}[/tex]
Hence,
The leading coefficient will be
[tex]-\frac{52}{2000}[/tex]
