Question

question 3 (1 point) an equation with real coefficients has 1 - i, 3, and 4 among its roots. what is the lowest possible degree of the equation? 3 5 4 6

Explanation:

Step1: Identify conjugate root

For polynomials with real coefficients, complex roots come in conjugate pairs. Given root $1-i$, its conjugate $1+i$ must also be a root.

Step2: Count distinct roots

The roots are $1-i$, $1+i$, $3$, $4$. This gives 4 distinct roots.

Step3: Determine lowest degree

The degree of a polynomial is equal to the number of its roots (counting multiplicities). For the lowest degree, we take each root once, so degree = 4.

Answer:

$\boldsymbol{4}$ (Option: ○ 4)