Question

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

Answer 1

    2x^2 - 5x + 3 = 0

=> 2x^2/2 - 5x/2 + 3/2 = 0    (dividing both sides by 2)

=> x^2 - 5x/2 + 3/2 = 0

=> [x^2 - 5x/2 + (5/4)^2] - (5/4)^2 + 3/2 = 0

=> [x - 5/4]^2 - 25/16 + 3/2 = 0

=> [x - 5/4]^2 - (25-24/16) = 0

=> [x - 5/4]^2 - 1/16 = 0

=> [x - 5/4]^2 = 1/16

=> x - 5/4 = 1/4   (square rooting on both sides)

=> x = 1/4 + 5/4

=> x = (1+5/4)

=> x = 6/4

=> x = 3/2

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here, we have

⇒ 2x² - 5x + 3 = 0

Dividing equation by 2, we get

⇒ x² - 5/2x + 3/2 = 0

Shifting the constant term on RHS

⇒ x² - 5/2x = - 3/2

Adding (1/2 coefficient of x)² on both sides

⇒ (x - 5/4)² = 25/16 - 3/2

⇒ (x - 5/2)² = 1/16

⇒ x - 5/4 = ± 1/4 or x = 5/4 - 1/4 = 4/4

⇒ x = 3/2, 1

Hence, the roots of the equation 2x² - 5x + 3 = 0 are 3/2 and 1.