Q:

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.

Accepted Solution

A:
The relationship between the values of m and n for the trinomial x²+bx -c is (m+n) is the sum of the roots and (mn) is the product of the roots.What is trinomial?A trinomial is the type of algebraic expression in which there are three terms present and more than one variable are present.The trinomial given in the problem is,[tex]x^2 +bx - c[/tex]This trinomial has factors of,[tex](x +m)(x - n),[/tex]Where m, n, and b are positive.If this factors multiply by each other, we get,[tex](x +m)(x - n)\\x^2+nx+mx+nm\\x^2+(n+m)x+nm[/tex]Compare it with the trinomial, we get,[tex]b=(m+n)[/tex] Which is the sum of the terms,[tex]c=nm[/tex]Which is the product of the terms.Hence, the relationship between the values of m and n for the trinomial x²+bx -c is (m+n) is the sum of the roots and (mn) is the product of the roots.Learn more about the trinomial here;