The equation 2m^(2)-1m-8=0 has solutions of the form M= N +or- sqaure root of D/over M Solve this equation and find the appropriate values of N,M,and D. Do not worry about simpl…

Question

The equation
`2m^(2)-1m-8=0` has solutions of the form

M= N +or- sqaure root of D/over M


Solve this equation and find the appropriate values of N,M,and D. Do not worry about simplifying the √D portion of the solution.


N= M= D=

Answer 1

• N = 1
• M = 4
• D = 65

Explanation:

The given equation is of the form ...

ax² +bx +c = 0

where a=2, b=-1, c=-8.

The quadratic formula gives the solution to the above equation as ...

`x=(-b\pm√(b^2-4ac))/(2a)`

So, for your equation, the solution is ...

`m=(-(-1)\pm√((-1)^2-4(2)(-8)))/(2(2))=(1\pm√(65))/(4)`

Comparing this to the form ...

`m=(N\pm√(D))/(M)`

we see ...

• N = 1
• M = 4
• D = 65