Find a positive number that equals 42 when added to it's square
1 answer:
if the number is x, then
the positive number, when added to its square (remember, its=posessive and it's is a constraction), equals 42
this can be writen as
perfect, we need to solve by making one side 0 and then factoring since if ab=0, we can assume and solve for a and b by saying that a=0 and b=0
minus 42 from both sides
now, either use the quadratic formula or complete the square or factor
I will factor
find what 2 numbers multiply to get -42 and add to get 1 (since the linear coefient is 1 and the constant is -42)
those numbers are -6 and 7
factor
set each to 0
x-6=0
x=6
x+7=0
x=-7, false since we wanted a positive number
the number is 6
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Using the Factor Theorem, the polynomials are given as follows:
1.
2.
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
<h3>What is the Factor Theorem?</h3>The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
Item a:
The parameters are:
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
Item b:
The roots are:
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
Item 3:
The roots are:
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
More can be learned about the Factor Theorem at brainly.com/question/24380382
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The line passes through and
. We can compute the slope as