Question

Factor and solve the quadratic equation 4x² - 9 = 0.

A) x = 3/2, x = -3/2
B) x = 3, x = -3
C) x = 2, x = -2
D) x = 4, x = -4

Answer 1

The quadratic equation 4x² - 9 = 0 is factored into (2x + 3)(2x - 3) = 0, yielding solutions x = 3/2 and x = -3/2.

Step-by-step explanation:

The given quadratic equation is 4x² - 9 = 0. This can be factored into the form (ax + b)(ax - b) which is a difference of squares. In this case, (2x + 3)(2x - 3) = 0. We set each factor equal to zero and solve for x, which gives us x = 3/2 and x = -3/2.

To factor the equation, we recognize that 4x² can be written as (2x)² and that 9 is 3², so the equation is a difference of two squares: (2x)² - 3² = 0. Thus, the factored form is (2x + 3)(2x - 3) = 0. To find the solutions for x, we set each factor equal to zero: 2x + 3 = 0 and 2x - 3 = 0. Solving these, we get x = -3/2 and x = 3/2, respectively.