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The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.

Verified Answer :

cssoldier2002

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 :

\(x^2+bx-c\)

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

\(x+m=0\\x=-m\\\\x-n=0\\x=n\)

Quadratic equation of the form

\(ax^2+bx+c=0\\The sum of roots = \frac{-b}{a} \\\)

the roots are -m and n

sum of roots

\(-m+n=\frac{-b}{1} \\b=m-n\)

The product of roots = c/a

\(-m(n)=\frac{c}{1} \\c=-mn\)

Learn more :  brainly.com/question/2734110

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