Answer:
The last equation x2 - 2x -4 = 0
has solution (x - 1)^2 - 5 = 0, x = 1 + root(5) or x = 1 - root(5)
Step-by-step explanation:
If a quadratic function has roots 1 and 5
f(x) = (x -1)(x- 5)
f(x) = x^2 - 6x + 5
Unless you meant. -4 and 6 ?
g(x) = (x + 4)(x - 6)
g(x) = x^2 -2x -24
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Or did you mean x = 1 and x =4 ?...
x^2 + 2x + 4 = 0 : complete square x^2 + 2x + 1 + 3 = 0, (x+1)^2 + 3 = 0
x^2 - 2x + 4 = 0 : complete square: (x -1)^2 + 3 = 0
0x^2 + 2x - 4 = 0, 2x - 4 = 0, x = 2
x^2 - 2x - 4 = 0 becomes: x^2 - 2x + 1 - 1 -4 = 0 ; (x - 1)^2 - 5 = 0
Answer:
6 = A, 2 = B, -5 = C
Step-by-step explanation:
Computing an integral by substitution is the reverse of the chain rule for computing the derivative. Substitution is intended to rewrite a complicated-looking integral involving the derivative of some component expression as another much simpler integral. For example, if
, then
and

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Integration by parts is the reverse of the product rule for derivatives:

Integrating both sides with respect to
gives


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Personally, I think the best way to grasp the idea behind the two methods is to practice. You start to notice patterns to the point where knowing which is the "right" method to use becomes second nature.
Art teachers use their eyes and judge the art.