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Inessa05 [86]
2 years ago
7

The quadratic function g(x)=ax^2+bx+c has the complex roots (-7+4i) and (-7-4i)

Mathematics
1 answer:
Stells [14]2 years ago
4 0

Answers:

a = 1

b = 14

c = 65

===========================================================

Explanation:

Let's focus on the root x = -7+4i

Add 7 to both sides, then square both sides. Then get everything to one side so 0 is on the other side.

x = -7+4i

x+7 = 4i

(x+7)^2 = (4i)^2

(x+7)^2 = 16i^2

(x+7)^2 = 16(-1)

(x+7)^2 = -16

(x+7)^2+16 = 0

If you were to follow those steps for the other root -7-4i, then you should get the same result. Solving (x+7)^2+16 = 0 leads to the two complex roots -7+4i and -7-4i.

Expand out that expression to get it into standard form

(x+7)^2+16

(x+7)(x+7)+16

x^2+7x+7x+49+16

x^2+14x+65

The equation is now in y = ax^2+bx+c form

a = 1

b = 14

c = 65

If you were to plug those a,b,c values into the quadratic formula, you'll find that it leads to the two given roots -7+4i and -7-4i.

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Answer:

We failed to reject H₀

Z > -1.645

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Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: p = 0.40

Alternate hypotheses = H₁: p < 0.40

Determine the level of significance and Z-score:

Given level of significance = 1% = 0.01

Since it is a lower tailed test,

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Determine type of test:

Since the alternate hypothesis states that less than 40% of U.S. cell phone owners use their phone for most of their online browsing, therefore we will use a lower tailed test.

Select the test statistic:  

Since the sample size is quite large (n > 30) therefore, we will use Z-distribution.

Set up decision rule:

Since it is a lower tailed test, using a Z statistic at a significance level of 1%

We Reject H₀ if Z < -1.645

We Reject H₀ if p ≤ α

Compute the test statistic:

$ Z =  \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }}  $

$ Z =  \frac{0.31 - 0.40}{ \sqrt{\frac{0.40(1-0.40)}{100} }}  $

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Conclusion:

We failed to reject H₀

Z > -1.645

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We failed to reject H₀

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