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

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Answer 1 · 2015-07-16T02:33:03

The discriminant is zero. It tells you that there are two identical 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

$4/3x^2 – 2x +3/4 = 0$

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

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.

What is the discriminant of 4/3x^2 - 2x + 3/4 = 04/3x^2 - 2x + 3/4 = 0 and what does that mean?