Question

A quadratic function has the complex roots 3 + 2ż. What is the equation of the function in

standard form? The value of a is given as 1 for this quadratic.
f(x)=x²+bx+c
b=?
c=?

Answer 1

To determine the values of b and c in the quadratic equation f(x) = x² + bx + c with complex roots, we use the fact that complex roots come in conjugate pairs. The quadratic function with the given root 3 + 2i and its conjugate 3 - 2i will be x² - 6x + 13.

Step-by-step explanation:

The subject of this question is Mathematics, specifically working with quadratic functions and complex roots. Given a quadratic function with complex roots and a leading coefficient of 1 (a = 1), we can find the values of b and c in the quadratic equation of the form f(x) = x² + bx + c. Since complex roots come in conjugate pairs, the other root must be 3 - 2i. Using these roots, we can create the factors of the quadratic equation: (x - (3 + 2i)) and (x - (3 - 2i)). Multiplying these out, we will get x² - 6x + 13 as the quadratic equation in standard form. Therefore, b = -6 and c = 13.