Quadratic Inequalities
Akopọ
You can already solve a quadratic equation. A quadratic inequality asks a related but richer question: for which values of x is the expression positive, or negative? The answer is no longer a couple of points but a whole range of values, and finding that range turns out to be elegant once you see the structure.
In this lesson you will solve inequalities like \(x^2-x-6>0\) by first finding the roots, then deciding which regions satisfy the inequality using a quick sketch or a sign diagram. You will learn to express answers in the two standard shapes examiners expect: a single interval like \(-3
Awọn Afojusun
- Find the solution set for quadratic inequalities, either graphically or algebraically.
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Oriire fun ipari ẹkọ lori Quadratic Inequalities. 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.
- What is the solution of x^2 - x - 6 > 0? A. -2 < x < 3 B. x < -2 or x > 3 C. -3 < x < 2 D. x < 2 or x > 3 Answer: B
- What is the solution of x^2 - x - 12 < 0? A. x < -3 or x > 4 B. -3 < x < 4 C. -4 < x < 3 D. x < 3 or x > 4 Answer: B
- The roots of a quadratic with a > 0 are -1 and 5. Where is the expression negative? A. x < -1 or x > 5 B. -1 < x < 5 C. x > 5 D. x < -1 Answer: B
- The roots of a quadratic with a > 0 are 2 and 6. Where is the expression positive? A. 2 < x < 6 B. x < 2 or x > 6 C. x < 6 D. x > 2 Answer: B
- Which of these is a valid way to write the solution of a quadratic inequality? A. -2 > x > 3 B. x < -2 or x > 3 C. 3 < x < -2 D. x = -2 or x = 3 Answer: B
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