Question

Solve for x using the master product method in the equation 6x² - 19x + 10 = 0. a) x = 2, x = 5/3

b) x = 5/2, x = 2
c) x = 5/3, x = 2/3
d) x = 5, x = 2/3

Answer 1

To solve the equation 6x² - 19x + 10 = 0 using the master product method, factorize the quadratic equation by grouping the terms. The solutions to the equation are x = 5/2 and x = 2/3.

Step-by-step explanation:

To solve the equation 6x² - 19x + 10 = 0 using the master product method, we need to factorize the quadratic equation. First, we multiply the coefficient of x² (6) by the constant term (10) to get 60. We need to find two numbers whose product is 60 and whose sum is the coefficient of x (-19). These numbers are -4 and -15.

Next, we replace the middle term (-19x) with -4x and -15x to get 6x² - 4x - 15x + 10 = 0. Now, we can group the terms and factor by grouping. This gives us (6x² - 4x) - (15x - 10) = 0.

Factoring out the common factors, we get 2x(3x - 2) - 5(3x - 2) = 0. Now, we have a common factor of (3x - 2). Factoring it out, we get (2x - 5)(3x - 2) = 0.

To find the solutions, we set each factor equal to zero and solve for x. So, we have 2x - 5 = 0 and 3x - 2 = 0. Solving these equations, we find x = 5/2 and x = 2/3.