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lesya692 [45]
2 years ago
6

Find a quadratic polynomial each with the given number as the sum and product of its zeros respectively

Mathematics
2 answers:
Pavlova-9 [17]2 years ago
8 0

Answer:

The answer is 4x² – x – 4 = 0

Step-by-step explanation:

<h2>1st Method </h2><h3><u>Given</u>;</h3>
  • Sum of zeroes = α + β = (-b)/a = 1/4
  • Product of zeros = αβ = c/a = 1

Where,

  • a = 4
  • b = 1
  • c = 4

So, one quadratic polynomial satisfying is given condition is 4x² – x – 4 = 0

<h2>2nd Method</h2>

Sum of zeroes = 1/4

Product of zeros = 1

Remember this formula

x² – (α + β)x + αβ

x² – 1/4x + 1

4x² – x – 4 = 0

Thus, The quadratic polynomial is

4x² – x – 4 = 0.

NARA [144]2 years ago
5 0

Step-by-step explanation:

sum of zeroes = 1/4

product of its zeros = 1

so,

4x^2- x - 4

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Consider the following information related to a set of quantitative sample data:
svlad2 [7]

Answer:

(a) There are outliers

(b) x and x >62

Step-by-step explanation:

Given

\sigma = 14.92

\bar x = 22.0

q_0 = -24

q_1 = 14.5

q_2 = 24.5

q_3 = 33.5

q_4 = 64

Solving (a): Check for outliers

This is calculated using:

Lower = Q_1 - (1.5 * IQR) --- lower bound of outlier

Upper = Q_3 +(1.5 * IQR) --- upper bound of outlier

Where

IQR = Q_3 - Q_1

So, we have:

IQR = 33.5 - 14.5

IQR = 19

The lower bound of outlier becomes

Lower = Q_1 - (1.5 * IQR)

Lower = 14.5 - (1.5 * 19)

Lower = 14.5 - 28.5

Lower = -14

The upper bound of outlier becomes

Upper = Q_3 +(1.5 * IQR)

Upper = 33.5 + 1.5 * 19

Upper = 33.5 + 28.5

Upper = 62

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-14 \le x \le 62 --- the range without outlier

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q_0 = -24  --- This represents the lowest data

q_4 = 64   --- This represents the highest data

-24 and 64 are out of range of -14 \le x \le 62.

Hence, there are outliers

Solving (b): The outliers

The outliers are data less than the lower bound (i.e. less than -14) or greater than the upper bound (i.e. 62)

So, the outliers are:

x and x >62

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3 years ago
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