Answer:
Roots: x = 5; x = 4
Step-by-step explanation:
Given the quadratic equation, x² -9x + 20 = 0
where a = 1, b = -9, and c = 20
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (-9)² - 4(1)(20) = 1
Since b² - 4ac > 0, then it means that the equation will have two real roots.
Use the Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]x = \frac{-(-9) +/- \sqrt{(-9)^{2} - 4(1)(20)} }{2(1)}[/tex]
[tex]x = \frac{9 +/- \sqrt{1}}{2}[/tex]
[tex]x = \frac{9 + 1}{2}; x = \frac{9 - 1}{2}[/tex]
[tex]x = \frac{10}{2}; x = \frac{8}{2}[/tex]
x = 5; x = 4
Therefore, the roots of the quadratic equation are: x = 5; x = 4.
