What is the discriminant of #x^2 -11x + 28 = 0# and what does that mean?

1 Answer
Jul 16, 2015

Answer:

The discriminant is 9. It tells you that there are two 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

#x^2 -11x +28 = 0#

#Δ = b^2 – 4ac = 11^2 -4×1×28 = 121 – 112 = 9#

This tells you that there are two real roots.

We can see this if we solve the equation.

#x^2 -11x +28 = 0#

#(x-7)(x-4) = 0#

#(x-7) = 0 or #(x-4) = 0#

#x=7# or #x = 4#

There are two real roots to the equation.