How do you find the discriminant for #9x^2+24x=-16# and determine the number and type of solutions?

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Answer 1 · 2018-04-12T01:21:13

See a solution process below:

First, write the equation in standard form:

#9x^2 + 24x + color(red)(16) = -16 + color(red)(16)#

#9x^2 + 24x + 16 = 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)(24)# for #color(blue)(b)#

#color(green)(16)# for #color(green)(c)#

#color(blue)(24)^2 - (4 * color(red)(9) * color(green)(16))#

#576 - (36 * color(green)(16))#

#576 - 576#

#0#

Because the discriminate is #0# there is just one solution to this problem.