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amm1812
3 years ago
12

We want to find the zeros of this polynomial p(x)= ( x^2-1)(x^2-5x+6)

Mathematics
1 answer:
Scrat [10]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

To find the zeros let p(x) = 0 , that is

(x² - 1)(x² - 5x + 6) = 0

Factorise each factor

x² - 1 ← is a difference of squares and factors as (x - 1)(x + 1)

x² - 5x + 6 = (x - 2)(x - 3), thus

(x - 1)(x + 1)(x - 2)(x - 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 1 = 0 ⇒ x = - 1

x - 2 = 0 ⇒ x = 2

x - 3 = 0 ⇒ x = 3

The zeros are x = ± 1, x = 2, x = 3

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A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be shown. If an examinee
katrin [286]

Answer: A) 1260

Step-by-step explanation:

We know that the number of combinations of n things taking r at a time is given by :-

^nC_r=\dfrac{n!}{(n-r)!r!}

Given : Total multiple-choice questions  = 9

Total open-ended problems=6

If an examine must answer 6 of the multiple-choice questions and 4 of the open-ended problems ,

No. of ways to answer 6 multiple-choice questions

= ^9C_6=\dfrac{9!}{6!(9-6)!}=\dfrac{9\times8\times7\times6!}{6!3!}=84

No. of ways to answer 4 open-ended problems

= ^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6\times5\times4!}{4!2!}=15

Then by using the Fundamental principal of counting the number of ways can the questions and problems be chosen = No. of ways to answer 6 multiple-choice questions x No. of ways to answer 4 open-ended problems

= 84\times15=1260

Hence, the correct answer is option A) 1260

5 0
3 years ago
Two students, Matt and Billy , each calculated the volume of a spherical ball with a dime tee of 15 centimeters. Their work is s
Aleksandr-060686 [28]

Answer:

Matt ;

Used diameter of the ball instead of Radius

Step-by-step explanation:

The volume of a sphere is given as :

4/3πr³

Radius, r = diameter / 2

Given that, the diameter = 15 cm ; The Radius = 15 / 2 = 7.5 cm

Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.

By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.

7 0
2 years ago
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umka21 [38]

Answer:

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Step-by-step explanation:

6 0
3 years ago
State whether the slope of the line is positive, negative, zero, or undefined.
Rudiy27

The slope of the line is equal to \tan \alpha, where angle \alpha is angle of line incline to the positive x-direction.

  • When \alpha is acute, then slope is positive;
  • When \alpha is obtuse, then slope is negative;
  • When \alpha is right, then slope is undefined;
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In your case angle of inclination is obtuse and slope is negative.

Answer: correct choice is B


7 0
3 years ago
Read 2 more answers
At a particular restaurant, each pizza roll has 60 calories and each mini hotdog has 70 calories. A combination meal with pizza
PolarNik [594]

Answer:

There are 9 pizza rolls and 12 mini hotdogs in the meal.

Step-by-step explanation:

We are given the following in the question.

Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.

Total number of items in combination meal = 21

Thus, we can write the equation:

x + y = 21

Calorie in a pizza roll = 60

Calorie in a mini hotdog = 70

Total calories = 1380

Thus, we can write the equation:

60x + 70y = 1380

Solving the two equations, we get,

60x + 70y - (60x+60y) = 1380 - 60(21) \\10y = 120\\\Rightarrow y = 12\\\Rightarrow x = 21-12 = 9

Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.

4 0
3 years ago
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