Final answer:
To write a quadratic equation in the form x² + bx + c = 0 with roots -7 ± 5i, we can use the fact that complex roots come in conjugate pairs. The quadratic equation is x² + 14x + 74 = 0.
Step-by-step explanation:
To write a quadratic equation in the form x² + bx + c = 0 with roots -7 ± 5i, we can use the fact that complex roots come in conjugate pairs. The roots are -7 + 5i and -7 - 5i. Therefore, the equation can be written as (x - (-7 + 5i))(x - (-7 - 5i)) = 0.
Expanding this equation, we get (x + 7 - 5i)(x + 7 + 5i) = 0. Multiplying these binomials, we have (x + 7)² - (5i)² = 0.
Simplifying further, we get x² + 14x + 49 - 25i² = 0. Since i² = -1, the equation simplifies to x² + 14x + 49 + 25 = 0.
Therefore, the quadratic equation in the form x² + bx + c = 0 with roots -7 ± 5i is x² + 14x + 74 = 0.