What is the discriminant of -8x^2+4x−1 and what does that mean?

1 Answer
Yahia M.
Apr 12, 2018

discriminant =#-16#
It means that the polynomial has no real solutions

Explanation:

the discriminant is a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial
consider a function #ax^2+bx+c=0#

in order to find the values of #x# that satisfies the equation We use the following formula

#x=(-b+-sqrt(b^2-4ac))/(2a)#

where #b^2-4ac# is the discriminant
if
#b^2-4ac>0# then the equation has two real solutions
#b^2-4ac=0# then the equation has one real solution
#b^2-4ac<0# then the equation has no real solution

so in the equation #-8x^2+4x-1=0#
by substituting in the discriminant formula with
#a=-8 ,b=4 ,c=-1#

#b^2-4ac=16-4(-8xx-1)=-16##<0#
so the functions will have no real solutions
(but it will have imaginary solutions)

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