What is the discriminant of #4/3x^2 - 2x + 3/4 = 0# and what does that mean?

1 Answer
Jul 16, 2015

Answer:

The discriminant is zero. It tells you that there are two identical real roots to the equation.

Explanation:

If you have a quadratic equation of the form

#ax^2+bx+c=0#

The solution is

#x = (-b±sqrt(b^2-4ac))/(2a)#

The discriminant #Δ# is #b^2 -4ac#.

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

  • If #Δ > 0#, there are two separate real roots.
  • If #Δ = 0#, there are two identical real roots.
  • If #Δ <0#, there are no real roots, but there are two complex roots.

Your equation is

#4/3x^2 – 2x +3/4 = 0#

#Δ = b^2 – 4ac = (-2)^2 -4×4/3×3/4 = 4 – 4 = 0#

This tells you that there are two identical real roots.

We can see this if we solve the equation.

#4/3x^2 – 2x +3/4 = 0#

#16x^2 -24x +9 = 0#

#(4x-3)(4x-3) = 0#

#4x-3 = 0# and #4x -3 = 0#

#4x = 3# and #4x = 3#

#x = 3/4# and # x = 3/4#

There are two identical roots to the equation.