Solving x² - 4x + 13 = 0

Algebra 2 · Axiom Academy

EXAMPLE Solving x^2 - 4x + 13 = 0 Using the quadratic formula when the discriminant is negative Solve x^2 - 4x + 13 = 0 using the quadratic formula. Great work! You've learned how to solve quadratic equations with complex solutions. Remember: Check the discriminant first: if , you'll have complex solutions Use : this lets you simplify square roots of negative numbers Complex conjugates: solutions always come in pairs, a + bi and a - bi Standard form: write complex numbers as a + bi , where a is the real part and b is the imaginary coefficient This example's pair: x = 2+3i and x = 2-3i share the same real part ( 2 ) and have opposite imaginary parts ( +3i and -3i ) Complex numbers are essential in advanced mathematics, physics, and engineering. You've just taken an important step in expanding your mathematical toolkit!

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