Solving Quadratic Equations by using the Quadratic Formula?

Question

4m^2+3m=1

Answer 1

Question Number 1 :

For this equation 4*m^2 + 3*m  = 1 , answer the following questions :

A. Find the roots using Quadratic Formula !

Answer Number 1 :

First, we have to turn equation : 4*m^2 + 3*m  = 1 , into a*x^2+b*x+c=0 form.

4*m^2 + 3*m  = 1 , move everything in the right hand side, to the left hand side of the equation

<=> 4*m^2 + 3*m  - ( 1 ) = 0 , which is the same with

<=> 4*m^2 + 3*m  + ( - 1 ) =0 , now open the bracket and we get

<=> 4*m^2 + 3*m - 1 = 0

The equation 4*m^2 + 3*m - 1 = 0 is already in a*x^2+b*x+c=0 form.

By matching the constant position, we can derive that the value of a = 4, b = 3, c = -1.

1A. Find the roots using Quadratic Formula !

  By using abc formula the value of x is both

    m1 = (-b+sqrt(b^2-4*a*c))/(2*a) and m2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  Since a = 4, b = 3 and c = -1,

  we need to subtitute a,b,c in the abc formula, with thos values.

  So we get m1 = (-(3) + sqrt( (3)^2 - 4 * (4)*(-1)))/(2*4) and m2 = (-(3) - sqrt( (3)^2 - 4 * (4)*(-1)))/(2*4)

  Which make m1 = ( -3 + sqrt( 9+16))/(8) and m2 = ( -3 - sqrt( 9+16))/(8)

  Which make m1 = ( -3 + sqrt( 25))/(8) and m2 = ( -3 - sqrt( 25))/(8)

  It imply that m1 = ( -3 + 5 )/(8) and m2 = ( -3 - 5 )/(8)

  We get following answers m1 = 0.25 and m2 = -1

Answer 2

Quadratic Formula

-b±√(b^2 - 4ac)

____________

           2a

Given:

4m^2 + 3m = 1

Remember: a = 4m^2, b = 3m, c = 1

1) 4m^2 + 3m -1 = 0

2) -3±√[(3^2) - 4(4)(-1)]

____________

           2(4)

3) -3±√9 + 16

____________

           8

4) -3±√25

____________

           8

5) -3±5

____________

           8

Possible answers:

a) positive: 1/4

b) negative: -1