Answer: The correct option is 4.
Explanation:
It is given that the polynomial has two zeros at x=-4 and x=7.
If a polynomial has zeros at x=c then (x-c) is a factor of the polynomial.
Since the polynomial has two zeros at x=-4 and x=7, therefore the polynomial has factor (x+4) and (x-7).
[tex]P(x)=(x+4)(x-7)[/tex]
[tex]P(x)=x(x-7)+4(x-7)[/tex]
[tex]P(x)=x^2-7x+4x-28[/tex]
[tex]P(x)=x^2-3x-28[/tex]
This equation is represented by option 4, therefore the option 4 is correct and the equation [tex]P(x)=x^2-3x-28[/tex] has zeros at x = –4 and x = 7.
