Solving Quadratic Equations
Bayani Gaba-gaba
The quadratic equation is one of the most important in all of mathematics, and there is more than one way to crack it. Factorisation is fast when it works, the formula always works, and completing the square reveals the structure that makes the formula possible. A skilled student knows all three and chooses the right tool for each equation.
In this lesson you will solve quadratics by factorising, by the quadratic formula \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\), and by completing the square. You will see worked examples of each and learn which method to reach for first.
Manufura
- Solve quadratic equations for real roots by factorisation, by the quadratic formula and by completing the square.
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Barka da kammala darasi akan Solving Quadratic Equations. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
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- Solve x^2 - 5x + 6 = 0. A. x = 1 or x = 6 B. x = 2 or x = 3 C. x = -2 or x = -3 D. x = 5 or x = 6 Answer: B
- Which expression is the quadratic formula? A. (-b +/- sqrt(b^2 - 4ac))/2a B. (-b +/- sqrt(b^2 + 4ac))/2a C. (b +/- sqrt(b^2 - 4ac))/a D. (-b +/- sqrt(4ac - b^2))/2a Answer: A
- Completing the square, x^2 + 6x + 5 equals: A. (x + 3)^2 - 4 B. (x + 3)^2 + 4 C. (x + 6)^2 - 5 D. (x + 3)^2 - 9 Answer: A
- Solve x^2 + 6x + 5 = 0. A. x = 1 or x = 5 B. x = -1 or x = -5 C. x = -1 or x = 5 D. x = 3 only Answer: B
- For 2x^2 - 4x - 3 = 0, the value of b^2 - 4ac is: A. -8 B. 16 C. 40 D. 4 Answer: C
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Sashen littafi
Quadratic Equations
Solve quadratic equations by factoring.
"College Algebra: Quadratic Equations" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/2-5-quadratic-equations. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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