Solving Quadratic Equations
Gbogbo ọrọ náà
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.
Ebumnobi
- Solve quadratic equations for real roots by factorisation, by the quadratic formula and by completing the square.
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Ekele diri gi maka imecha ihe karịrị na Solving Quadratic Equations. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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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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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Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Solving Quadratic Equations? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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