Final answer:
To solve the quadratic equation x² + 2x + 10 = 0, we use the quadratic formula, applying the values a = 1, b = 2, and c = 10. The solutions are complex because the discriminant (b² - 4ac) is negative. The solution set is d: {-1 +3i, -1−3i}.
Step-by-step explanation:
The student is asking for the solution set of the quadratic equation x² + 2x + 10 = 0 using the quadratic formula. The general form of a quadratic equation is ax² + bx + c = 0, and the quadratic formula to find the roots of the equation is:
x = −b ± √(b² − 4ac) / (2a)
In this case, a = 1, b = 2, and c = 10. Applying these values to the quadratic formula, we get:
x = −(2) ± √((2)² − 4∙1∙10) / (2∙1)
Which simplifies to:
x = −(2) ± √(4 − 40) / 2
Since 4 minus 40 results in a negative number, we will have complex solutions:
x = −(2) ± √(−36) / 2
√(−36) can be written as 6i, where i is the imaginary unit. Therefore:
x = −(2) ± 6i / 2
Simplifying further gives:
x = −(1) ± 3i