4. what are the zeros of the polynomial function y= 2x2-3x+1?
a. 1/2,1
b. -2,1
c. -1, -5
d. -1, -1/5

A

Step-by-step explanation:

Given

y = 2x² - 3x + 1

To find the zeros let y = 0, that is

2x² - 3x + 1 = 0

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 1 = 2 and sum = - 3

The factors are - 2 and - 1

Use these factors to split the x- term

2x² - 2x - x + 1 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) - 1(x - 1) = 0 ← factor out (x - 1) from each term

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

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =

x - 1 = 0 ⇒ x = 1

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.