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2 years ago

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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3 years ago

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3 years ago

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

$Upper = Q_3 +(1.5 * IQR)$

$Upper = 33.5 + 1.5 * 19$

$Upper = 33.5 + 28.5$

$Upper = 62$

So, we have:

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

Given that:

$q_0 = -24$ --- 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