Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.

₹0.0

Question: Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.

Options:

Correct Answer: x = 3

Solution:

This can be factored as (2x - 3)(2x - 3) = 0. Thus, x = 3.

Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.

Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.

Step 1: Write down the quadratic equation: 4x^2 - 12x + 9 = 0.
Step 2: Identify the coefficients: a = 4, b = -12, c = 9.
Step 3: Check if the equation can be factored. Look for two numbers that multiply to (a * c) = 4 * 9 = 36 and add to b = -12.
Step 4: The numbers -6 and -6 work because -6 * -6 = 36 and -6 + -6 = -12.
Step 5: Rewrite the middle term using these numbers: 4x^2 - 6x - 6x + 9 = 0.
Step 6: Group the terms: (4x^2 - 6x) + (-6x + 9) = 0.
Step 7: Factor out the common terms: 2x(2x - 3) - 3(2x - 3) = 0.
Step 8: Factor by grouping: (2x - 3)(2x - 3) = 0.
Step 9: Set each factor equal to zero: 2x - 3 = 0.
Step 10: Solve for x: 2x = 3, so x = 3/2.
Step 11: Since both factors are the same, the root is x = 3/2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring, the quadratic formula, or completing the square.
Factoring – Recognizing how to factor a quadratic expression correctly and identifying repeated roots.
Roots of Equations – Finding the values of x that satisfy the equation, which are also known as the roots.