How do you find the discriminant and how many and what type of solutions does #6x^2=13x# have?

1 Answer
May 10, 2015

Ripan's solutions are correct but don't answer the more general question.

Solutions to a quadratic of the form #ax^2+bx+c=0# are given by
the quadratic formula #(-b+-sqrt(b^2-4ac))/(2a)#

The sub-expression within the square root determines the number (and type) of solutions; this sub-expression is called the "discriminant" and is typically expressed as:
#Delta = b^2-4ac#
with the conditions
#Delta { (< 0 " there are no Real solutions"),(=0" there is 1 Real solution"),(>0" there are 2 Real solutions"):}#

Given #6x^2=13x#
we can re-arrange this into the general form
#6x^2-13x+0 = 0#

and
#Delta = (13)^2 -4(6)(0) = 169>0#
so #6x^2= 13x# has 2 Real solutions