How do you find the value of the discriminant and determine the nature of the roots #-4r^2-4r=6#?

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Answer 1 · 2017-07-24T10:28:16

See a solution process below:

First, put this equation in standard form:P

#-4r^2 - 4r - color(red)(6) = 6 - color(red)(6)#

#-4r^2 - 4r - 6 = 0#

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)(-4)# for #color(red)(a)#

#color(blue)(-4)# for #color(blue)(b)#

#color(green)(-6)# for #color(green)(c)#

Giving:

#color(blue)(-4)^2 - (4 * color(red)(-4) * color(green)(-6))#

#16 - 96#

#-80#

Because the Discriminate is negative you get a complex solution.