Fractions in the Answer
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 31 of 51.
When a is not 1, the bottom of the formula, 2a, is no longer 2, and the parts often come out as fractions. Take 9x^2 + 6x + 5 = 0: a is 9, b is 6, c is 5, and b^2 - 4ac is 36 - 180, which is -144. Its root is 12i.
So x = (-6 ± 12i)/18. Divide each term of the top by 18 and reduce: -6 over 18 is -(1/3), and 12 over 18 is 2/3. The solutions are x = -(1/3) + (2/3)i and x = -(1/3) - (2/3)i.
Why divide term by term? The form a + bi names the real part and the imaginary part separately, so each gets its own fraction, reduced. A common slip is to reduce one term and forget the other.
Challenge
Solve 4x^2 + 4x + 5 = 0 with the quadratic formula. Write each solution as a + bi.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
2Completing the Square
Perfect Square TrinomialsThe Missing NumberCompleting the SquareIrrational AnswersWhen a Is Not 1Recap: Completing the Square5Complex Arithmetic
Adding and SubtractingMultiplyingThe ConjugateDividingA Pure Imaginary BottomRecap: Complex Arithmetic8Lines Meet Parabolas
Two CrossingsJust TouchingNo MeetingA Circle and a LineRecap: Lines and Parabolas3Vertex Form by Algebra
From Standard to VertexOdd Middle TermsA Leading NumberOpening DownRecap: Vertex Form6Complex Solutions
Squares Equal to NegativesA Shifted SquareThe Formula Goes ComplexFractions in the AnswerRecap: Complex Solutions