Question

complex numbers & higher order polynomials practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
solve the equation ( x^2 - 5x + 10 = 0 ). express your solution(s) as a conjugate pair using ( pm ) (1 point)
( x = square pm square )
check answer remaining attempts: 3

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = -5\), \(c = 10\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(x=\frac{-(-5)\pm\sqrt{(-5)^2 - 4(1)(10)}}{2(1)}\)

Step3: Simplify discriminant

Calculate discriminant: \(\Delta = 25 - 40=-15\)
So \(x=\frac{5\pm\sqrt{-15}}{2}=\frac{5\pm i\sqrt{15}}{2}\) (since \(\sqrt{-15}=i\sqrt{15}\))

Step4: Express as conjugate pair

Rewrite as \(x = \frac{5}{2}\pm\frac{\sqrt{15}}{2}i\)

Answer:

\(x=\frac{5}{2}\pm\frac{\sqrt{15}}{2}i\) (or in the boxed form as per the question's format: first box \(\frac{5}{2}\), second box \(\frac{\sqrt{15}}{2}i\))