Answer:
The leading coefficient is 3
Step-by-step explanation:
Polynomials
Given the roots of a polynomial x1,x2,x3, it can be expressed as:
[tex]p(x)=a(x-x1)(x-x2)(x-x3)[/tex]
Where a is the leading coefficient.
We are given the roots x1=-6, x2=7i, x3=-7i, thus:
[tex]p(x)=a(x+6)(x-7i)(x+7i)[/tex]
Operating the product of the conjugated imaginary roots:
[tex]p(x)=a(x+6)(x^2+49)[/tex]
Knowing p(2)=1,272 we can find the value of a
[tex]p(2)=a(2+6)(4+49)=1,272[/tex]
Operating:
[tex]a(8)(53)=1,272[/tex]
[tex]424a=1,272[/tex]
Solving:
[tex]a=1,272/424[/tex]
a=3
The leading coefficient is 3
