Question

Determine the number and types of solutions for

6m^2-3m-4=0

Answer 1

Given:

The equation is

`6m^2-3m-4=0`

To find:

The number and types of solutions for the given equation.

Solution:

We have,

`6m^2-3m-4=0`

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
`ax^2+bx+c=0`, if
`b^2-4ac>0`, then the equation has two distinct real solutions.

For the given equation, a=6, b=-3 and c=-4.

`D=b^2-4ac`

`D=(-3)^2-4(6)(-4)`

`D=9+96`

`D=105>0`

Therefore, the given equation has two distinct real solutions.