What is the distance between the roots of this equation?

(x+4)(x-6)=0​

10 units

Step-by-step explanation:

Given

(x + 4)(x - 6) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 6 = 0 ⇒ x = 6

The roots are x = - 4 and x = 6

Use the absolute value to find the distance between them, that is

| - 4 - 6 | = | - 10 | = 10 , or

| 6 - (- 4) | = | 6 + 4 | = | 10 | = 10

The distance between the roots is 10 units

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0