One root of the quadratic equation x^2 − 2x + m = 0 is 9. If the other root is n, what is n−m?
x^2-2x+m = (x-9)(x-n)
so,
-2 = -(n+9)
m = 9n
n = -7
m = -63
m+n = -70
thanks a lot steve
To find the value of n−m, we need to first determine the values of m and n.
We are given that one root of the quadratic equation x^2 − 2x + m = 0 is 9. This means that when we substitute x = 9 into the equation, it should equal zero.
Plugging x = 9 into the equation:
(9)^2 − 2(9) + m = 0
Simplifying this equation gives:
81 − 18 + m = 0
63 + m = 0
Therefore, m = -63.
Now that we have the value of m, we can proceed to find the value of n. In a quadratic equation, the sum of the roots is given by the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the coefficient of the linear term is -2 and the coefficient of the quadratic term is 1.
The sum of the roots, n + 9, is equal to -(-2)/1 = 2. From this, we can conclude that n + 9 = 2.
Subtracting 9 from both sides of the equation, we find:
n = 2 - 9 = -7
Now, to find n - m:
n - m = (-7) - (-63)
= -7 + 63
= 56
Therefore, n - m = 56.