How do you find the discriminant and how many and what type of solutions does 6x^2=13x6x2=13x have?

1 Answer
Alan P.
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=0ax2+bx+c=0 are given by
the quadratic formula (-b+-sqrt(b^2-4ac))/(2a)−b±√b2−4ac2a

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

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