Answer:
[tex]4x^2-16=0[/tex]
Step-by-step explanation:
We want to write the quadratic equation whose roots are 2 and -2, and whose leading coefficient is 4.
Since 2 and -2 are roots, [tex]x+2\\and\\x-2[/tex] are factors of this quadratic function.
The factored form is given as: [tex]a(x-2)(x+2)=0[/tex]
Since the leading coefficient is 4, a=4
Therefore the equation becomes:
[tex]4(x-2)(x+2)=0[/tex]
Recognize and expand using difference two squares.
[tex]4(x^2-4)=0[/tex]
The required equation is:
[tex]4x^2-16=0[/tex]
