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How do you find the value of the discriminant and state the type of solutions given #4k^2+5k+4=-3k#?

Answer 1

Nathan Axel

#Delta = 0#
#1# repeated root

rearrange the equation into the form #ak^2+bk+c=0#:

#4k^2+5k+4=-3k#
#4k^2+5k+3k+4=0#
#4k^2+8k+4=0#

divide both sides by #4#:
#k^2+2k+1=0#

#ak^2+bk+c=0#
#k^2+2k+1=0#

#therefore a=1, b=2, c=1#

#Delta# (discriminant) #= (b^2-4ac)# for a quadratic equation

here, #b^2-4ac = 2^2-(4*1*1)#
#=4-4#
#=0#

#0=0#
since #Delta=0, k# has #1# repeated root.

on a graph:

the parabola only meets the #x#-axis once- there is only #1# root.

through factorisation:

#k^2+2k+1=0#
#(k+1)(k+1)=0#
solving for #k#, you get
'#k = -1# or #k=-1#'

the number #-1# is repeated, giving the name 'repeated root'.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.