Find the X-Intercepts: Solving the Quadratic Equation x² - 6x + 5

Video Solution

Solution Steps

00:00 Find the coordinates of points A,B

00:03 Notice that points A,B are the intersection points with the X-axis

00:07 At the intersection points with the X-axis, the Y value must = 0

00:15 Substitute Y = 0 and solve for X values

00:21 Break down the function into a trinomial

00:28 This is the corresponding trinomial

00:32 Find what zeros each factor in the product

00:36 This is one solution

00:40 This is the second solution

00:46 And this is the solution to the question

Step-by-Step Solution

To solve for the points A and B, we need to find the roots of the function $f(x) = x^2 - 6x + 5$ where $f(x) = 0$ .

Let's proceed step-by-step:

Step 1: Set the function to zero
We begin by setting the equation to zero: $x^2 - 6x + 5 = 0$ .
Step 2: Factor the quadratic
We need to factor the expression. We look for two numbers that multiply to $c = 5$ and add to $b = -6$ . These numbers are $-1$ and $-5$ .
Step 3: Write the factorization
Therefore, we can write the quadratic as: $(x - 1)(x - 5) = 0$ .
Step 4: Solve for the roots
Set each factor equal to zero: \begin{align*} x - 1 &= 0 \\ x &= 1 \end{align*} \begin{align*} x - 5 &= 0 \\ x &= 5 \end{align*} The roots are $x = 1$ and $x = 5$ .
Step 5: Identify the Points A and B
The points A and B, where the function intersects the x-axis, are $(1, 0)$ and $(5, 0)$ .

Thus, the coordinates of points A and B are $(1,0),(5,0)$ , which matches choice 1.