The given line passes through the points and (4, 1).
1 answer:
9514 1404 393
Answer:
y +3 = 1/2(x +4)
Step-by-step explanation:
The slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(4 -(-4)) = 4/8 = 1/2
The point-slope form of the equation for a line is ...
y -y1 = m(x -x1)
Filling in the known values, this is ...
y -(-3) = 1/2(x -(-4))
y +3 = 1/2(x +4)
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Answer:
Step-by-step explanation:
There are 6 solutions or zeros here because, according to the Fundamental Theorem of Algebra, the degree of the polynomial dictates how many zeros there are in the polynomial. If we had a 3rd degree polynomial, we would expect to find 3 zeros; if we had a 5th degree polynomial, we would have 5 zeros, etc. The easiest way to factor this is to do it initially by grouping:
then
then
We will factor each set of parenthesis now to get all the zeros. For the first set of parenthesis:
so
so
But since we can't have a negative under the square root, we have to offset it by using the imaginary number i. i-squared = -1, so
x = ±i√5
Those are the first 2 zeros out of 6. Now for the second set of parenthesis:
4x⁴ - 25 = 0. That is the difference between perfect squares, and that factors to this:
(2x² + 5)(2x² - 5)
The first set of parenthesis there:
2x² + 5 = 0 so
2x² = -5 so
x² = -5/2 so
x = ±
Those are the next 2 zeros. We found 4 so far, now we will find the last 2 in the second set of parenthesis above:
so
so
x = ±
In summary, the 6 zeros are as follows:
x = , -
,
,
,
,