Question

practice assignment 5.1 quadratic functions
question 8
solve the equation: (m^2 - 3m + 9 = 0). fully simplify all answers, including non-real solutions.
(m =)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify coefficients

For the equation \( m^2 - 3m + 9 = 0 \):

$$ a = 1, \quad b = -3, \quad c = 9 $$

Step 2: Apply the quadratic formula

$$ m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ m = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(9)}}{2(1)} $$

$$ m = \frac{3 \pm \sqrt{9 - 36}}{2} $$

$$ m = \frac{3 \pm \sqrt{-27}}{2} $$

Step 3: Simplify the radical with complex numbers

$$ \sqrt{-27} = i\sqrt{27} = i\sqrt{9 \cdot 3} = 3i\sqrt{3} $$

$$ m = \frac{3 \pm 3i\sqrt{3}}{2} $$

Answer:

\( m = \frac{3 \pm 3i\sqrt{3}}{2} \) (or written as \( \frac{3}{2} \pm \frac{3\sqrt{3}}{2}i \))