Question

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.

Answer 1

m,n are positive so $m\geq n$ is the required relationship between values of m & n.

Step-by-step explanation:

Here we have , The binomial x2 + bx – c or $x^2 +bx -c$ has factors of (x + m)(x – n), where m, n, and b are positive. We need to find relationship between m & n :

$(x+m)(x-n)$

⇒ $(x+m)(x-n)$

⇒ $(x^2 +mx-nx-mn)$

⇒ $x^2 +(m-n)x-(mn)$

Comparing coefficients of this equation to  $x^2 +bx -c$ :

$m - n =b$ and $c = mn$

Also , discriminant of $x^2 +bx -c$ is greater then 0 i.e. $b^2-4(-c)\geq 0$

$b^2+4c\geq 0$

⇒ $b^2\geq -4c$

⇒ $(m-n)^2\geq -4mn$

⇒ $m^2-2mn+n^2\geq -4mn$

⇒ $m^2-2mn+4mn+n^2\geq0$

⇒ $(m+n)^2\geq0$

⇒ $m\geq -n$

Since, m,n are positive so $m\geq n$ is the required relationship between values of m & n.

Answer 2

Answer:

Answer for edge:

The value of m must be greater than the value of n.

The coefficient of the middle term, b, is the sum of m and –n.

The factor with the greater absolute value has the sign of the middle term.

Since b is positive, m must have the larger absolute value.

Step-by-step explanation: