How do you determine the value of k so that #4x^2 + 24x + k = 0# has discriminant zero?

1 Answer
Mar 19, 2017

Answer:

#k=color(green)(36)#

Explanation:

For the general quadratic: #ax^2+bx+c=0#
the discriminant is
#color(white)("XXX")Delta=b^2-4ac#

For the specific quadratic: #4x^2+24x+k=0#
the discriminant is
#color(white)("XXX")Delta=24^2-4 * 4 * k#

If we want the discriminant to be zero:
#color(white)("XXX")color(blue)(24^2)-color(magenta)(4 * 4 * k) = 0#

#color(white)("XXX")rarr color(blue)((4^2) * (6^2)) - color(magenta)((4^2) * k)=0#

#color(white)("XXX")rarr 6^2-k=0#

#color(white)("XXX")rarr k=6^2=36#