What is the discriminant of #9x^2-6x+1=0# and what does that mean?

1 Answer
Jul 27, 2015

Answer:

For this quadratic, #Delta = 0#, which means that the equation has one real root (a repeated root).

Explanation:

The general form of a quadratic equation looks like this

#ax^2 + bx + c = 0#

The discriminant of a quadratic equation is defined as

#Delta = b^2 - 4 * a * c#

In your case, the equation looks like this

#9x^2 - 6x + 1 = 0#,

which means that you have

#{(a=9), (b=-6), (c=1) :}#

The discriminant will thus be equal to

#Delta = (-6)^2 - 4 * 9 * 1#

#Delta = 36 - 36 = color(green)(0)#

When the discrimiannt is equal to zero, the quadratic will only have one distinct real solution, derived from the general form

#x_(1,2) = (-b +- sqrt(Delta))/(2a) = (-6 +- sqrt(0))/(2a) = color(blue)(-b/(2a))#

In your case, the equation has one distinct real solution equal to

#x_1 = x_2 = -((-6))/(2 * 9) = 6/18 = 1/3#