Question

Samuel factored the quadratic equation 4x^2 - 18x + 20 = 0 as (u - 5)(u - 4) = 0, where u^2 = 4x^2. Determine which of the following are solutions to 4x^2 - 18x + 20 = 0.

a) u = -2
b) u = -4
c) u = 0
d) u = 8

Answer 1

To determine which values of u are solutions to the quadratic equation 4x^2 - 18x + 20 = 0, we substitute each value of u into the equation and check if it satisfies the equation. The only value of u that satisfies the equation is u = 0.

Step-by-step explanation:

To determine which of the given values of u are solutions to the quadratic equation 4x^2 - 18x + 20 = 0, we need to substitute each value of u into the equation and check if it satisfies the equation.

Given that u^2 = 4x^2, we can rewrite the equation as (u - 5)(u - 4) = 0. We can then substitute each value of u into this equation and check if it equals zero.

1. Let u = -2: Substituting -2 into the equation, we get (-2 - 5)(-2 - 4) = 7(-6) = -42, which is not equal to zero. Therefore, u = -2 is not a solution.
2. Let u = -4: Substituting -4 into the equation, we get (-4 - 5)(-4 - 4) = -9(-8) = 72, which is not equal to zero. Therefore, u = -4 is not a solution.
3. Let u = 0: Substituting 0 into the equation, we get (0 - 5)(0 - 4) = -5(-4) = 20, which is equal to zero. Therefore, u = 0 is a solution.
4. Let u = 8: Substituting 8 into the equation, we get (8 - 5)(8 - 4) = 3(4) = 12, which is not equal to zero. Therefore, u = 8 is not a solution.

From the above analysis, the only value of u that is a solution to the quadratic equation 4x^2 - 18x + 20 = 0 is u = 0.