Quadratic formula
factoring
graphing
completing the square
factoring by grouping
Rational Roots Theorem
synthetic division
Take a look at <span>5x^2 – 34x + 24 = 0. The last term could have been the result of these different possible muliplications: 1*24, 2*12, 3*8, 4*6. The leading term is 5, whose factors are 5 and 1. Thus, possible rational roots would be
4/5 (the 4 is a factor of 24 and the 5 is a factor of 5) and 6/1 (the 6 is a factor of 24 and the 1 is a factor of 5).
Using synth. div. to check whether 6 is actually a root:
___________________
6 / 5 -34 24
30 -24
------ --------------------------
5 -4 0
since the remainder is 0, we can safely call 6 a "root."
Note the remaining coefficients, 5 and -4:
They correspond to the factor 5x - 4. If we set this difference = to 0, and solve for x, we get x = 4/5 (which is correct).
The roots of </span><span>5x^2 – 34x + 24 = 0 are x = 4/5 and x= 6/1.</span>
Answer:
L'(4, -4)
Step-by-step explanation:
When you're given a midpoint, you can find the point equidistant on the other side of the midpoint by subtracting the relevant coordinate from <em>double that of the midpoint</em>.
Here, the line of reflection is the horizontal line y=-1, so you know only the y-coordinate will change. The reflected point will be ...
(x, y) ⇒ (x, -2-y)
so the point of interest is ...
L' = (4, -2-2) = (4, -4)
