the trinomial $x^{2}+bx - c$ has factors of $(x + m)(x - n)$, where $m$, $n$, and $b$ are positive. what is…

the trinomial $x^{2}+bx - c$ 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.

the trinomial $x^{2}+bx - c$ 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.

Answer

Explanation:

Step1: Expand the factors

$(x + m)(x - n)=x^{2}-nx+mx - mn=x^{2}+(m - n)x - mn$

Step2: Compare with the trinomial

Since $x^{2}+(m - n)x - mn=x^{2}+bx - c$, then $b=m - n$.

Step3: Use the condition of positive - valued $b$

Given $b>0$, so $m - n>0$.

Answer:

$m>n$