Question

4. Find the roots of the equation 5x2
-6x-2=0 by the method of completing the square.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution :-

5x² - 6x - 2 = 0

⇒ 5x² - 6x = 2

Dividing throughout by 5

⇒ 5x²/5 - 6x/5 = 2/5

⇒ x² - 6x/5 = 2/5

It can be written as

⇒ x² - 2( x )( 3/5 ) = 2/5

Adding ( 3/5 )² on both sides

⇒ x² - 2( x )( 3/5 ) + ( 3/5 )² = 2/5 + ( 3/5 )²

⇒ (x - 3/5)² = 2/5 + 3² / 5²

[ Because (a + b)² = a² - 2ab + b² ]

⇒ (x - 3/5)² = 2/5 + 9/25

⇒ (x - 3/5)² = (10 + 9)/25

⇒ (x - 3/5)² = 19/25

Taking square root on both sides

⇒ x - 3/5 = ± √19/25

⇒ x - 3/5 = ± √19 / 5

⇒ x - 3/5 = √19 / 5 or x - 3/5 = - √19 / 5

⇒ x = √19 / 5 + 3/5 or x = 3/5 - √19 / 5

⇒ x = (√19 + 3)/5 or x = (3 - √19)/5

Therefore the roots of the equation are (√19 + 3)/5 and (3 - √19)/5.