Mathematics, 22.07.2019 21:00 lydialinton23

Use the rational root theorem to list all possible rational roots for the equation. x^3+2x-9=0.

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Rational root theorem:

Given a polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_0$ , the rational roots are +- $\frac{r_0}{r_n}$ where r_0

= factor of the constant a_0

and

= factors of the leading coefficient a_n

.

So, to find the possible rational roots, we list all the factors of the constant and the leading coefficients and then set up the ratios.
In this case, the constant is a_0=–9

and the leading coefficient is a_n=1

.
Factors of –9: +-1, +-3, +-9
Factors of 1: +-1

Thus, the possible rational roots are +-1/1, +-3/1, +-9/1
or +-1, +-3, +-9.

+-1, +-3, +-9

Answer from: aidan0824

Using the Rational Roots(Zeros) Theorem, which states that, if the polynomial $f(x) = a_nx^n + a_{n-1} x^{n-1} +...+ a_1x + a_0$ has integer coefficients, then every rational zero of f(x) has the form $\dfrac{p}{q}$ where is a factor of the constant term a_0 and is a factor of the leading coefficient a_n. .

f(x) = x^3 + 2x - 9

Here,

$p: \pm1,\pm3, \pm9$ which are all factors of constant term

$q: \pm1$ which are the factors of the leading coefficient

All possible values are

$\dfrac{p}{q}: \pm1, \pm3, \pm9$

f(x) = x^3 + 2x - 9

f(1) = 1 + 2 - 9 = -6

f(-1) = -1 -2 -9 = -12

f(3) = 27 + 6 -9 = 24

No values are leading to zeros hence, none of these can be roots of the equation.

Learn more about rational root theorem here:

link

Answer from: Quest

answer: segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality. in the case of brown v. board of education, that standard was challenged and defeated. segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to education. this was being violated by states whose laws supported the segregation of schools. section 1 of the 14th amendment reads as follows:

all persons born or naturalized in the united states and subject to the jurisdiction thereof, are citizens of the united states and of the state wherein they reside. no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united states; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Answer from: Quest

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!

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