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3 years ago

Find the roots of the given polynomial equation.

Mathematics

2 answers:

bija089 [108]3 years ago

6 0

Answer:

Consider x^ {2}-4x+3. Factor the expression by grouping. First, the expression needs to be rewritten as x^ {2}+ax+bx+3. To find a and b, set up a system to be solved. a=-3 b=-1. Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system so

Step-by-step explanation:

Maksim231197 [3]3 years ago

6 0

9514 1404 393

Answer:

-1, 1, 2 (multiplicity 2)
-7, -5, 3

Step-by-step explanation:

Just as you find it easiest to ask someone else to find the roots for you, I find it easiest to use a graphing calculator to find the roots. It shows the roots to be ...

-1, 1, 2 (multiplicity 2)
-7, -5, 3

If you're searching for roots by hand, the usual process is to make a guess based on Descartes' Rule of Signs, and the Rational Root Theorem. Then factor out that root using synthetic division or long division to reduce the polynomial degree.

This has 3 sign changes, so 1 or 3 positive real roots. If odd-degree terms change signs, there is one sign change, indicating 1 negative real root. The Rational root theorem tells you the rational roots will be divisors of 4:

±1, ±2, ±4

Both even-degree terms and odd-degree terms have coefficients that sum to zero. This indicates that 1 and -1 are both roots of the equation. Factoring those out gives ...

(x -1)(x +1)(x^2 -4x +4) = 0

The quadratic is a perfect square, so the full factorization is ...

(x +1)(x -1)(x -2)² = 0

Roots are -1, 1, and 2 (multiplicity 2).

The rule of signs tells you there is one positive real root and 0 or 2 negative real roots. The rational roots will be divisors of 105, so will be any of ...

±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105

Various other ways of estimating roots suggest the magnitudes will be less than ∛105 +√1 +9 ≈ 14.7. The sum of coefficients tells you the positive root is greater than 1. Trying x=3 shows that to be the positive real root. Factoring it out gives ...

(x -3)(x² +12x +35) = 0

The quadratic can be further factored, so we have ...

(x -3)(x +5)(x +7) = 0

Roots are -7, -5, and 3.

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pogonyaev

12
You want to find an equivalent ratio with 2:3. As the question already gives you 8 where 2 used to be, you need to find out what change occurred to get from 2 to 8 (a multiplication of 4). To find the missing part of the ratio, multiply 4 with 3 to get 12.

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3 years ago

Read 2 more answers

PLEASE HELP <br> I forgot how to do this and it’s for a final :((

natima [27]

F(x)= 2/(x+1) and g(x)= -x2-12 => f(-7)= ? , g(2.5)= ?, g(f(- 0.5))= ?
In the expression of the function f(x) we will replace instead of x the number in bracket (-7) => f(-7) = 2/(-7+1)= 2/-6 = - 1/3
In the expression of the function g(x) we will replace instead of x number in bracket (2.5) => g(2.5) = - (2.5)squared -12= - 6.25 -12= - 18.25
Expression f(g(x)) or g(f(x)) is multiplication (composition) of the reflecting of functions f and g. We will do this in the following way => g(f(x))= g(2/(x+1))= -(2/(x+1))2 - 12= -(4/(x+1)2) -12= -4-12(x+1)2/(x+1)2=> we will replace instead of x the number in bracket (-0.5) or (-1/2) => g(f(-1/2) = -4-12((-1/2)+1)2/ ((-1/2+ 1)2= -4-12(1/2)2/(1/2)2=-4-12*(1/4)/(1/4)= (-4-3)/(1/4)=-28
Eaisier way => f(-1/2)=2/((-1/2)+1)=2/(1/2)= 4 g(4) -(4)2-12 = -16-12= -28

8 0

4 years ago

a restaurant worker used 5 loaves of wheat and 2 loaves of rye bread to make sandwiches for an event.what does the ratio 7:2 mea

kvasek [131]

The ratio 7: 2 means the total loaves of loaves to the total loaves of rye bread.

total loaves : Rye
7 : 2

7 0

3 years ago

A teacher gave a 3-question multiple choice quiz. Each question had 4 choices to select from. If the a student completely guesse

goldenfox [79]

Answer:

0.9844

Step-by-step explanation:

This is a binomial probability problem.

Probability of getting a correct answer: p = 1/4

Probability of getting an incorrect answer: q = 3/4

Number of questions; n = 3

Thus;

probability of 2 or less correct answers is; P(x ≤ 2) = P(X = 2) + P(X = 1) + P(X = 0)

From binomial probability the formula is;

P(X = x) = C(n, x) × p^(x) × q^(n - x)

P(X = 2) = C(3, 2) × (¼)² × (¾)¹

P(X = 2) = 3 × 0.0625 × 0.75

P(X = 2) = 0.1406

P(X = 1) = C(3, 1) × (¼)¹ × (¾)²

P(X = 1) = 3 × 0.25 × 0.5625

P(X = 1) = 0.4219

P(X = 0) = C(3, 0) × (¼)^(0) × (¾)³

P(X = 0) = 0.4219

P(x ≤ 2) = 0.1406 + 0.4219 + 0.4219

P(x ≤ 2) = 0.9844

4 0

3 years ago

Make a flow chart showing that the triangles below are similar. NO LINKS OR CRAZY LANGUAGES.!!!!!!

pantera1 [17]

Answer: See the attached image

You have the correct idea for the boxes you've filled out. For the first three boxes in column 1, I would be specific which segments you are dividing. So for instance, in the first box, it would be EG/EB = 55/11 = 5. Then the second box would be EF/EC = 35/7 = 5, and so on. The order of the boxes doesn't matter. The three boxes then combine together to help show that the triangles are similar. Specifically $\triangle EFG \sim \triangle ECB$ . The order of the letters is important to help show how the angles pair up and how the sides pair up. We use the SSS similarity theorem here.

The second problem is the same idea, but we use one pair of congruent angles. So we'll use the SAS similarity theorem this time.

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3 years ago