How do you find the value of the discriminant and determine the nature of the roots #8x^2 – 2x – 18 = -15 #?

Question

How do you find the value of the discriminant and determine the nature of the roots #8x^2 – 2x – 18 = -15  #?

Savannah Anderson · Accepted Answer

The discriminant of the second degree equation #ax^2+bx+c=0#is:
#b^2-4*a*c#

and the solutions depend on whether the two values #+- sqrt(b^2-4*a*c)#, are real or not

The given equation in the standard form #ax^2+bx+c=0# is #8x^2-2x-3=0# Then, #+- sqrt(b^2-4*a*c)# in our case is #+- sqrt((-2)^2-4*(8)*(-3))=+-sqrt(100)=+-10#. the value of the discriminant is 100, so the two values of the square root are real, and there are two real solutions to the equation.

Avery Alexander · Answer

There are 2 real roots which are irrational and distinct (different)

Make the quadratic equation = 0. #8x^2 -2x-3 = 0 larr # this is in the form #ax^2 +bx + c = 0# The discriminant is given by # Delta = b^2 - 4ac# #Delta = (-3)^2 - 4(8)(-3) = 9+96 = 105# What does this value of 105 tell us? #Delta > 0 rarr# there are 2 distinct (different) real roots. #Delta = 105 # which is not a perfect square #rarr # the roots are irrational. There are 2 real roots which are irrational and distinct (different)