Question

Without solving, determine the character of the solutions of the equation in the complex number system.9x² - 24x + 16 = 0Choose the correct answer below.O A. Two complex conjugate solutionsOB. Two unequal real-number solutionsO C. One repeated real-number solution

Answer 1

Step 1:

Write the equation

`9x^(22)\text{ - 24x + 16 = 0}`

Step 2:

Write the quadratic equation formula

`\begin{gathered} ax^2\text{ + bx + c = 0} \\ \text{x = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

Step 3:

a = 9, b = -24 and c = 16

`\begin{gathered} \text{x = }\frac{-(-24)\text{ }\pm\sqrt[]{(-24)^2-4*9*16}}{2*9} \\ \text{x = }\frac{24\pm\sqrt[]{576\text{ - 576}}}{18} \\ \text{x = }\frac{24\text{ }\pm\text{ }\sqrt[\square]{0}}{18} \\ \text{x = }\frac{\text{24 }\pm\text{ 0}}{18} \\ \text{x = }(24-0)/(18)\text{ or }\frac{24\text{ + 0}}{2} \\ \text{x = }(4)/(3)\text{ twice} \end{gathered}`

Final answer

C. One repeated real-number solution