To answer this question we have that the two roots of the equations are:
x = 5 ---> (5, 0)
x = -5 ---> (-5, 0)
If we factor them, we can write the quadratic expression as follows:
[tex](x-5)(x+5)[/tex]
And we have that the leading term is 4. Then, the quadratic equation is:
[tex]4(x-5)(x+5)[/tex]
If we expand this result, we have:
[tex]4(x^2-5^2)=4(x^2-25)=4x^2-4\cdot25=4x^2-100[/tex]
Then, the expanded quadratic expression is 4x²-100.
We can graph the result as follows (notice the values for each root):
In summary, we have that the quadratic equation whose roots are 5, and -5, and whose leading coefficient is 4, is as follows:
[tex]4(x-5)(x+5)[/tex]
If we expand the expression, we have:
[tex]4x^2-100[/tex]
