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lys-0071 [83]
3 years ago
11

Find a quadratic equation with roots -1, 4i and -1 - 4i

Mathematics
1 answer:
vazorg [7]3 years ago
3 0
\bf \textit{difference of squares}
\\\\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
\textit{also recall that }i^2=-1\\\\
-------------------------------\\\\
\begin{cases}
x=-1+4i\implies &x+1-4i=0\\
x=-1-4i\implies &x+1+4i=0
\end{cases}
\\\\\\
(x+1-4i)(x+1+4i)=\stackrel{y}{0}
\\\\\\\
[(x+1)~~-~~(4i)][(x+1)~~+~~(4i)]=y
\\\\\\\
[(x+1)^2~~-~~(4i)^2]=0\implies (x^2+2x+1)~-~(4^2i^2)=y
\\\\\\
(x^2+2x+1)~-~(16\cdot -1)=y\implies (x^2+2x+1)~-~(-16)=y
\\\\\\
x^2+2x+1~~+16=y\implies x^2+2x+17=y
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A. 1) Given
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8 0
2 years ago
A man drove his car a distance of 260 miles in 4 hours. If continuing at this rate is possible, he will travel ____ miles in 8 h
spayn [35]

Answer:

520 miles

Step-by-step explanation:

since 4 is half of 8, you just multiply 260 by 2.

4 0
3 years ago
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Algebra Question ( Matrices and Determinants ) 20 point
blagie [28]
The determinant of a 2 x 2 matrix can be calculated as:
Product of non-diagonal elements subtracted from product of diagonal elements.

The diagonal elements in given matrix are 12 and 2. The non-diagonal elements are -6 and 0.

So,

Determinant G = 12(2) - (-6)(0)

Determinant G = 24 - 0 = 24

So, option B gives the correct answer
6 0
3 years ago
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Need help asap will give brain and all non helpful answers will be reported
jonny [76]

Answer:

Local max is .5

Step-by-step explanation:

The local maximum is for x values between 2 and 4

It looks like the x value is 2.5 and the y value is .5


5 0
3 years ago
For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hou
Strike441 [17]

Answer:

Z = 1

Step-by-step explanation:

Z - score

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 61, \sigma = 4

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{65 - 61}{4}

Z = 1

4 0
3 years ago
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