How do you use the discriminant to determine the number of real-number solutions for #8x^2+8x+2=0#?

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Answer 1 · 2017-07-22T01:59:50

See a solution process below:

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)(8)# for #color(red)(a)#

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

#color(green)(2)# for #color(green)(c)#

#color(blue)(8)^2 - (4 * color(red)(8) * color(green)(2)) => 64 - 64 => 0#

Because the discriminate is #color(red)(0)# there will be just ONE solution.