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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 :

Step 1:

Write the equation

[tex]9x^{22}\text{ - 24x + 16 = 0}[/tex]

Step 2:

Write the quadratic equation formula

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

Step 3:

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

[tex]\begin{gathered} \text{x = }\frac{-(-24)\text{ }\pm\sqrt[]{(-24)^2-4\times9\times16}}{2\times9} \\ \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 = }\frac{24-0}{18}\text{ or }\frac{24\text{ + 0}}{2} \\ \text{x = }\frac{4}{3}\text{ twice} \end{gathered}[/tex]

Final answer

C. One repeated real-number solution