Question

solve the equation by the method of completing the square
$3x^2-5x+2 = 0$
​

Answer 1

Answer:

The zeroes are 2/3 and 1

Step-by-step explanation:

3x² - 5x + 2

First make the a = 1, divide by 3,

x² - 5x/3 +2/3

Taking the term b and dividing it by 2,

5/3 x 1/2 = 5/6

Making it a square with + and - signs

We get,

± (5/6)² --- (1)

Substituting (1) in the equation,

[x² - 5x/3 + (5/6)²] - (5/6)² + 2/3

By using the algebraic identity (a - b)² = a² - 2ab + b²

[x - 5/6]² - 25/36 + 24/36 = 0

[x - 5/6]² - 1/36 = 0

[x - 5/6]² = [1/6]²

x - 5/6 = ± 1/6

Therefore,

x = -1/6 + 5/6 = 4/6 = 2/3

x = 1/6 + 5/6 = 6/6 = 1

Therefore, the zeroes of the given quadratic equation is,

2/3, 1