The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 =

₹0.0

Question: The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 = 0. What is the value of a? (2021)

Options:

Correct Answer: 3

Exam Year: 2021

Solution:

The equation can be factored as (x - 3)^2 = 0, hence a = 3.

The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 = 0. What is the value of a? (2021)

The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 = 0. What is the value of a? (2021)

Step 1: Start with the quadratic equation x^2 - 6x + 9 = 0.
Step 2: Notice that the equation can be factored. We want to express it in the form (x - a)^2 = 0.
Step 3: Look for two identical numbers that multiply to 9 (the constant term) and add up to -6 (the coefficient of x).
Step 4: The numbers -3 and -3 work because -3 * -3 = 9 and -3 + -3 = -6.
Step 5: Therefore, we can write the equation as (x - 3)(x - 3) = 0.
Step 6: This simplifies to (x - 3)^2 = 0.
Step 7: From the expression (x - a)^2 = 0, we see that a = 3.

Factoring Quadratic Equations – The question tests the ability to factor a quadratic equation into a perfect square form.
Understanding Roots – It assesses the understanding of how to find the roots of a quadratic equation by setting it to zero.