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.
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;
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