Question

What are the roots of the polynomial equation 0 = x² - 26x + 48?

A) x = 24, x = 2
B) x = 12, x = 4
C) x = 6, x = 8
D) x = 10, x = 16

Answer 1

To find the roots of the equation 0 = x² - 26x + 48, we factored it into (x - 24)(x - 2) = 0 and solved for x, resulting in roots x = 24 and x = 2, corresponding to option A).

Step-by-step explanation:

The question asks to find the roots of the quadratic equation 0 = x² - 26x + 48. To solve this equation, we need to factor the quadratic or use the quadratic formula. The correct factoring of this particular equation is (x - 24)(x - 2) = 0. Setting each factor equal to zero gives us the solutions: x = 24 and x = 2. Therefore, the roots of the equation are x = 24 and x = 2, which corresponds to option A).

In general, for any quadratic equation of the form ax²+bx+c = 0, the roots can be found using the quadratic formula, which is:

x = ∛ b²-4ac

2a

However, in this case, since the quadratic equation was easily factorable, the use of the quadratic formula was not necessary. The roots found by factoring are the correct option in the final answer.