How do you use the discriminant to determine the nature of the roots for #-6x^2 - 12x + 90 = 0#?

1 Answer
Jun 19, 2015

Answer:

As here, #Delta>0 # and a perfect square there are two real rational roots.

Explanation:

# -6x^2 -12x +90 = 0#
The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=-6, b=-12, c=90#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-12)^2-(4*(-6)*90)#
# = 144+2160 =2304#

As here, #Delta>0# and it is also a perfect square there are two real rational roots.

  • Note :
    The solutions are normally found using the formula
    #x=(-b+-sqrtDelta)/(2*a)#

As #Delta = 2304#, #x = (-(-12)+-sqrt(2304))/(2*-6) = (12+-48)/-12#
# x = (12-48)/-12 = 36/12= color(green)(3#
# x = (12+48)/-12 = -60/12 =color(green)( -5#