−73+98i is a root of f(x)=x2+146x+14933. Find the other roots of f(x).Write your answer as a list of simplified values separated by commas, if there is more than one value.
Q. −73+98i is a root of f(x)=x2+146x+14933. Find the other roots of f(x).Write your answer as a list of simplified values separated by commas, if there is more than one value.
Complex Roots Conjugate Pairs: Since the coefficients of the polynomial are real numbers, the complex roots of polynomials with real coefficients come in conjugate pairs. This means that if −73+98i is a root, then its conjugate, −73−98i, must also be a root.
Sum of Roots Quadratic Equation: To find the other root, we can use the fact that the sum of the roots of a quadratic equationax2+bx+c=0 is equal to −ab. In this case, the sum of the roots is −146.
Setting up Equation for Other Root: We already know one of the roots is −73+98i, so we can set up the equation −146=(−73+98i)+other_root to solve for the other root.
Calculating Other Root: Subtracting the known root from −146 gives us the other root: other_root=−146−(−73+98i)=−146+73−98i=−73−98i.
Final Result: Therefore, the other root of the polynomial f(x) is −73−98i.