How do you find the value of the discriminant and determine the nature of the roots #3x² + 6x - 42 = 0#?

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Answer 1 · 2017-08-23T21:58:27

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)(3)# for #color(red)(a)#

#color(blue)(6)# for #color(blue)(b)#

#color(green)(-42)# for #color(green)(c)#

#color(blue)(6)^2 - (4 * color(red)(3) * color(green)(-42)) =>#

#36 - (-504) =>#

#36 + 504 =>#

#540#

Because the discriminate is positive, you will get two real solutions