How do you find the value of the discriminant and determine the nature of the roots #-9b^2=-8b+8#?

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Answer 1 · 2017-08-22T12:40:05

See a solution process below:

First, convert the equation to standard form:

#-9b^2 + color(red)(8b) - color(blue)(8) = -8b + 8 + color(red)(8b) - color(blue)(8)#

#-9b^2 + 8b - 8 = 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)(-9)# for #color(red)(a)#

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

#color(green)(-8)# for #color(green)(c)#

#color(blue)(8)^2 - (4 * color(red)(-9) * color(green)(-8))#

#64 - 288#

#-224#

Because the discriminate is negative there will be a complex solution.