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

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Answer 1 · 2015-07-16T19:20:11

The discriminant is 9. It tells you that there are two real roots to the equation.

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.

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.

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