To find the other solution to the quadratic equation x² – 6x + 8 = 0, we can use the fact that if x = 2 is one solution, we can factor the quadratic equation.
The factored form of a quadratic equation is expressed as (x – r₁)(x – r₂) = 0, where r₁ and r₂ are the roots (or solutions) of the equation.
Since we know one solution is x = 2, we can plug this into the factored form:
(x – 2)(x – r₂) = 0
Next, we can expand this expression to get back to the standard form:
x² – (2 + r₂)x + (2 * r₂) = 0
This must match our original equation:
x² – 6x + 8 = 0
From this, we see that:
- -(2 + r₂) = -6 → 2 + r₂ = 6 → r₂ = 4
- 2 * r₂ = 8 → 2 * 4 = 8
Thus, the other solution is x = 4. We can verify this by checking if substituting x = 4 satisfies the original equation:
4² – 6(4) + 8 = 0 → 16 – 24 + 8 = 0 → 0 = 0
This confirms that both 2 and 4 are indeed the solutions to the equation. Therefore, the other solution is x = 4.