How do you find the discriminant and how many and what type of solutions does #3x^2- 2x = 5# have?

2 Answers
May 3, 2015

#y = 3x^2 - 2x - 5 = 0.#
For this type of quadratic equations, you don't need to find the Discriminant.
Shortcut: When a - b + c = 0, one real roots is (-1) and the other is #(-c/a = 5/3).#
2 real roots: -1 and 5/3.

May 3, 2015

For a quadratic equation in the form
#ax^2 + bx + c = 0#
the discriminant is #Delta =b^2-4ac#

Convert the given equation into the "standard form"
#3x^2-2x = 5#

#rarr 3x^2-2x-5 =0#

#Delta = (-2)^2 - 4(3)(-5)#

#Delta = 4+60 = 64 = 8^2#

Since #Delta > 0#
the given equation has #2# Real solutions

The full form for roots of the quadratic
#(-b+-sqrt(Delta))/(2a)#

would become
#(2+-8)/(2(6))#
and both solutions would be Rational (but not Integers)