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

2 Answers
Nghi N.
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.

Alan P.
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)

Related questions
See all questions in Solutions Using the Discriminant
Impact of this question
2720 views around the world
You can reuse this answer
Creative Commons License