Question

Each root and constant of c

Answer 1

When we have a quadratic equation form ax² + bx + c = 0, we have rule
x₁ + x₂ = -b/a
x₁ × x₂ = c/a
x₁ and x₂ are the roots

Given from question:
⇒ x₂ = 2 + x₁
⇒ quadratic equation x² - 4x + c = 0

Solution A:
Determine a,b,c
a = 1
b = -4
c = c

Find the roots with the rule of x₁ + x₂ = -b/a
x₁ + x₂ = -b/a
x₁ + 2 + x₁ = -(-4)/1
2x₁ + 2 = 4
2x₁ = 4 - 2
2x₁ = 2
x₁ = 1
One of the roots is 1

Now find the other root
x₂ = 2 + x₁
x₂ = 2 + 1
x₂ = 3
The other root is 3

Solution B:
Find the constant c by the rule x₁ × x₂ = c/a
 x₁ × x₂ = c/a
1 × 3 = c
c = 3
The constant is 3