What is the discriminant of #m^2-8m=-14# and what does that mean?

1 Answer
Jun 17, 2018

Answer:

See a solution process below:

Explanation:

First, put the equation in standard quadratic form:

#m^2 - 8m = -14#

#m^2 - 8m + color(red)(14) = -14 + color(red)(14)#

#m^2 - 8m + 14 = 0#

or

#1m^2 - 8m + 14 = 0#

The quadratic formula states:

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

The discriminate is the portion of the quadratic equation within the radical: #color(blue)(b)^2 - 4color(red)(a)color(green)(c)#

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

#color(red)(1)# for #color(red)(a)#

#color(blue)(-8)# for #color(blue)(b)#

#color(green)(14)# for #color(green)(c)#

#color(blue)(-8)^2 - (4 * color(red)(1) * color(green)(14)) =>#

#64 - 56 =>#

#8#

Because the discriminate is Positive, you will get two real solutions.