Question

resolve into factors 4y^2-2y+1/4​

Answer 1

Answer:

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Given

The first term is, 4y2 its coefficient is 4 .

The middle term is, -2y its coefficient is -2 .

The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 4 • -1 = -4

Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -2 .

-4 + 1 = -3

-2 + 2 = 0

-1 + 4 = 3

Observation : No two such factors can be found !!

Solving 4y2-2y-1 = 0 by the Quadratic Formula .

According to the Quadratic Formula, y , the solution for Ay2+By+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

y = ————————

2A

In our case, A = 4

B = -2

C = -1

Accordingly, B2 - 4AC =

4 - (-16) =

20

Applying the quadratic formula :

2 ± √ 20

y = —————

8

Can √ 20 be simplified ?

Yes! The prime factorization of 20 is

2•2•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 20 = √ 2•2•5 =

± 2 • √ 5

√ 5 , rounded to 4 decimal digits, is 2.2361

So now we are looking at:

y = ( 2 ± 2 • 2.236 ) / 8

Two real solutions:

y =(2+√20)/8=(1+√ 5 )/4= 0.809

or:

y =(2-√20)/8=(1-√ 5 )/4= -0.309

Two solutions

y =(2-√20)/8=(1-√ 5 )/4= -0.309

y =(2-√20)/8=(1-√ 5 )/4= -0.309 y =(2+√20)/8=(1+√ 5 )/4= 0.809

Answer 2

Answer:

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