Solving Quadratic Equations
Akopọ
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.
Awọn Afojusun
- Solve quadratic equations for real roots by factorisation, by the quadratic formula and by completing the square.
Akọ̀wé Ẹ̀kọ́
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Ìdánwò Ẹ̀kọ́
Oriire fun ipari ẹkọ lori Solving Quadratic Equations. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
O wa lori ohun elo Green Bridge
Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.
Awọn Iwe Itọsọna Ti a Gba Nimọran
Ṣe Adaṣe Awọn Ibeere Idanwo Adaṣe
Ṣe o fẹ ṣe adaṣe awọn ibeere idanwo adaṣe nipa Solving Quadratic Equations? Ṣe igbasilẹ ohun elo Green Bridge CBT lati wọle si awọn ibeere idanwo adaṣe ati awọn ayẹwo adaṣe kikun fun koko-ọrọ yii.
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