Given:
The equation is
[tex]6m^2-3m-4=0[/tex]
To find:
The number and types of solutions for the given equation.
Solution:
We have,
[tex]6m^2-3m-4=0[/tex]
It is a 2nd degree polynomial because the highest degree of the variable x is 2.
Number of solutions = Degree of the polynomial
Number of solutions = 2
Therefore, the given equation has 2 solutions.
In a quadratic equation [tex]ax^2+bx+c=0[/tex], if [tex]b^2-4ac>0[/tex], then the equation has two distinct real solutions.
For the given equation, a=6, b=-3 and c=-4.
[tex]D=b^2-4ac[/tex]
[tex]D=(-3)^2-4(6)(-4)[/tex]
[tex]D=9+96[/tex]
[tex]D=105>0[/tex]
Therefore, the given equation has two distinct real solutions.
