Answer :
Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value
Answer:
b=m-n
c=-mn
Given :
[tex]x^2+bx-c[/tex]
the factor (x+m)(x-m)
Step-by-step explanation:
For factors (x+m) and (x-m) , the roots can be found by making factors =0 and solve for x
[tex]x+m=0\\x=-m\\\\x-n=0\\x=n[/tex]
Quadratic equation of the form
[tex]ax^2+bx+c=0\\The sum of roots = \frac{-b}{a} \\[/tex]
the roots are -m and n
sum of roots
[tex]-m+n=\frac{-b}{1} \\b=m-n[/tex]
The product of roots = c/a
[tex]-m(n)=\frac{c}{1} \\c=-mn[/tex]
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