# Determine the roots of 20x^2 - 22x + 6 = 0?

20x^2 - 22x + 6 = 0

### 8 Answers

- formengLv 62 months ago
Substituting into the quadratic formula will be as follows:

x =(-11+-sqrt(-11)^2 -4*10*6)/2*10)

Doing the arithmetic, this turns out to be as follows:

(-11+-sqrt (119)i)/20

- ?Lv 72 months ago
The discriminant

D=(-22)^2-4(20)(6)=4>0

The equation has 2 distinct real roots.

They are

x=[22+/-2]/(40)

=>

x=3/5 or x=1/2.

- la consoleLv 72 months ago
20x² - 22x + 6 = 0

20x² - 22x = - 6

x² - (22/20).x = - 6/20

x² - (11/10).x = - 3/10

x² - (11/10).x + (11/20)² = - (3/10) + (11/20)²

x² - (11/10).x + (11/20)² = 1/400

[x - (11/20)]² = 1/400

x - (11/20) = ± 1/20

x = (11/20) ± (1/20)

x = (11 ± 1)/20

x = (11 + 1)/20 = 12/20 = 3/5

x = (11 ± 1)/20 = 10/20 = 1/2

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- Engr. RonaldLv 72 months ago
20x^2 - 22x + 6 = 0

(4x - 2)(5x - 3) = 0

4x - 2 = 0, 5x - 3 = 0

x = 1/2 or x = 3/5

roots are 1/2 and 3/5..

- PuzzlingLv 72 months ago
Divide both sides by 2:

10x² - 11x + 3 = 0

Multiply the outside coefficients --> 10 * 3 = 30

You are looking for 2 numbers that multiply to be 30, but add to be the middle coefficient (-11). Obviously we need two negative numbers which are clearly -5 and -6.

Split the middle term into -5x and -6x:

10x² - 5x - 6x + 3 = 0

Factor each pair:

(10x² - 5x) - (6x - 3) = 0

5x(2x - 1) - 3(2x - 1) = 0

You have the repeated (2x - 1) so factor that out:

(5x - 3)(2x - 1) = 0

By the zero product rule, if ab=0 then a=0 or b=0:

5x - 3 = 0

5x = 3

x = 3/5

or

2x - 1 = 0

2x = 1

x = 1/2

Answer:

x = 1/2 or x = 3/5

Source(s): https://www.desmos.com/calculator/ifyodzg3ua