Question

5m^2-4m-2=0 solve by formula

Answer 1

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Quadratic equation : 5m² - 4m -2 = 0.

The quadratic formula = [ -b ±√( b² - 4ac ) ] / 2a

Here,

 a = coefficient of x² = 5

 b = coefficient of x = -4

 c = constant term = -2.

For 1st solution :

 ⇒ x = [ -b + √( b² - 4ac ) ] / 2a

 ⇒ x = [ -( -4 ) + √ {(-4)² - 4 × 5 × ( -2 ) } ] / 2 ( 5 )

 ⇒ x = [ 4 + √ ( 16 + 40 ) ] / 10

 ⇒ x = [ -4 + √56 ] / 10

 ⇒ x = [ 4 + 2√14 ] / 10

 ⇒ x = [ 2 ( 2 + √14 ) ] / 10

 ⇒ x = ( 2 + √14 ) / 5.

For another solution :

⇒ x = [ -b - √ ( b² - 4ac ) ] / 2a

⇒ x = [ - ( -4 ) - √ { ( -4 )² - 4 × 5 × ( -2 ) } ] / 2 × 5

⇒ x = [ 4 - √ ( 16 + 40 ) ] / 10

⇒ x = [ 4 - √56 ] / 10

⇒ x = [ 4 - 2√14 ] / 10

⇒ x = [ 2 ( 2 - √14 ) ] / 10

⇒ x = ( 2 - √14 ) / 5.

The zeroes are ( 2 + √14 ) / 5 and ( 2 - √14 ) / 5.


Hope it helps !!

Answer 2

Step-by-step explanation:

Quadratic equation : 5m² - 4m -2 = 0.

The quadratic formula = [ -b ±√( b² - 4ac ) ] / 2a

Here,

 a = coefficient of x² = 5

 b = coefficient of x = -4

 c = constant term = -2.

For 1st solution :

 ⇒ x = [ -b + √( b² - 4ac ) ] / 2a

 ⇒ x = [ -( -4 ) + √ {(-4)² - 4 × 5 × ( -2 ) } ] / 2 ( 5 )

 ⇒ x = [ 4 + √ ( 16 + 40 ) ] / 10

 ⇒ x = [ -4 + √56 ] / 10

 ⇒ x = [ 4 + 2√14 ] / 10

 ⇒ x = [ 2 ( 2 + √14 ) ] / 10

 ⇒ x = ( 2 + √14 ) / 5.

For another solution :

⇒ x = [ -b - √ ( b² - 4ac ) ] / 2a

⇒ x = [ - ( -4 ) - √ { ( -4 )² - 4 × 5 × ( -2 ) } ] / 2 × 5

⇒ x = [ 4 - √ ( 16 + 40 ) ] / 10

⇒ x = [ 4 - √56 ] / 10

⇒ x = [ 4 - 2√14 ] / 10

⇒ x = [ 2 ( 2 - √14 ) ] / 10

⇒ x = ( 2 - √14 ) / 5.

The zeroes are ( 2 + √14 ) / 5 and ( 2 - √14 ) / 5.