Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
M2 -2mn + n2 =
4 - (-16) + 16 =
20 + 16 = 36
Have a nice days.......
If the 3 points are collinear, then the slopes of all line segments connecting the points are the same.
Thus,
-6 - (-8) 2
m = ------------- = -------- = -1/2
-7 - (-3) -4
Then the following must be true:
4-(-6) 10
-1/2 = ------------ = ---------
c - (-7) c + 7
Cross multiplying, -(c+7) = 20, and c+7 = -20, so that c = -27
