Answer:
The quadratic equation is: [tex]x^2-11x+28=0\\[/tex]
Step-by-step explanation:
The quadratic equation with given solutions [tex]a[/tex] and [tex]b[/tex] can be written as:
[tex](x-a)(x-b)=0[/tex]
Given:
Solutions are 4 and 7.
The quadratic equation can be written as:
[tex](x-4)(x-7)=0\\[/tex]
We simplify it further to get it in standard form.
Using FOIL(Firsts Outsides Insides Lasts )
[tex](x\times x)+(x\times(-7))+((-4)\times x)+(-4\times(-7))=0\\\\x^2-7x-4x+28=0\\[/tex]
Combining like terms:
[tex]x^2-11x+28=0\\[/tex]
The quadratic equation is: [tex]x^2-11x+28=0\\[/tex]
