Question

5v squared - 6v + 1 = 0 solve using the quadratic formula

Answer 1

Answer:

$5 {v}^{2} - 6v + 1$

$5 {v}^{2} - 5v - v + 1$

$5v(v - 1) - 1(v - 1)$

$(v - 1)(5v - 1)$

Answer 2

Step-by-step explanation:

According to the Quadratic Formula, v , the solution for Av^2+Bv+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B^2-4AC

v = ————————

2A

In our case, A = 5

B = -6

C = 1

Accordingly, B^2 - 4AC

= 36 - 20

= 16

Applying the quadratic formula :

6 ± √ 16

v = —————

10

The prime factorization of 16 is

2×2×2×2

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).

√ 16 = √ 2×2×2×2

=2×2×√ 1

= ± 4 • √ 1

= ± 4

So now we are looking at:

v = ( 6 ± 4) / 10

Two real solutions:

v =(6+√16)/10=(3+2)/5= 1

or:

v =(6-√16)/10=(3-2)/5= 0.200

Hence,

Two solutions were found :

1. v = 1/5 = 0.200
2. v = 1

Hope this will help you

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