Question

4x^2 -9x +5 =0 do it using formula method and completing square method CAUTION : NO SPAMMERS ​

Answer 1

Solution :-

Method 1 : Formula method

4x² - 9x + 5 = 0

Comparing the given equation with ax² + bx + c = 0 we get,

• a = 4
• b = - 9
• c = 5

Discriminant D = b² - 4ac

⇒ D = ( - 9 )² - 4( 4 )( 5 )

⇒ D = 81 - 80

⇒ D = 1

Since b² - 4ac i.e Discriminant > 0 therefore the equation has two real and distinct roots

Now, find roots of the equation using quadratic formula

⇒ x = ( - b ± √D )/2a

Substituting the values

⇒ x = [ - ( - 9 ) ± √1 ] / 2( 4 )

⇒ x = (9 ± 1)/8

⇒ x = (9 + 1)/8 or x = (9 - 1)/8

⇒ x = 10/8 or x = 8/8

⇒ x = 5/4 or x = 1

Method 2 : Completing the square method

4x² - 9x + 5 = 0

⇒ 4x² - 9x = - 5

Dividing throughout by '4'

⇒ 4x²/4 - 9x/4 = - 5/4

⇒ x² - 9x/4 = - 5/4

It can be written as

⇒ x² - 2( x )( 9/8 ) = - 5/4

Adding ( 9/8 )² on both sides

⇒ x² - 2( x )( 9/8 ) + ( 9/8 )² = - 5/4 + ( 9/8 )²

⇒ (x - 9/8)² = - 5/4 + 81/64

[ Because a² - 2ab + b² = (a - b)² ]

⇒ (x - 9/8)² = ( -80 + 81 )/64

⇒ (x - 9/8)² = 1/64

Taking square root on both sides

⇒ x - 9/8 = ± √1/64

⇒ x - 9/8 = ± 1/8

⇒ x - 9/8 = 1/8 or x - 9/8 = - 1/8

⇒ x = 1/8 + 9/8 or x = - 1/8 + 9/8

⇒ x = 10/8 or x = 8/8

⇒ x = 5/4 or x = 1

Therefore the roots of the given equation are 5/4 and 1.