The Discriminant
Bayani Gaba-gaba
Before solving a quadratic, you can already tell how many real solutions it has, just from a single number buried inside the formula. That number is the discriminant, \(b^2-4ac\), and reading its sign is one of the quickest, most powerful checks in algebra.
In this lesson you will learn what the discriminant reveals about the roots of a quadratic: two distinct roots, one repeated root, or none at all. You will then use it to answer a favourite exam question, deciding whether a straight line cuts, touches or misses a curve, all without solving the equation fully.
Manufura
- Know the conditions for a quadratic equation to have two real roots, two equal roots or no real roots, using the discriminant.
- Use the related conditions for a given line to intersect, be a tangent to, or not intersect a given curve.
Takardar Darasi
Akwai a cikin manhajar Green Bridge
Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.
Nazarin Darasi
Barka da kammala darasi akan The Discriminant. Yanzu da kuka bincika mahimman raayoyi da raayoyi, 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.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- What is the discriminant of a quadratic ax^2 + bx + c = 0? A. b^2 + 4ac B. b^2 - 4ac C. 4ac - b^2 D. b - 4ac Answer: B
- If b^2 - 4ac > 0, the quadratic has: A. no real roots B. one repeated root C. two distinct real roots D. infinitely many roots Answer: C
- How many real roots has 2x^2 + 3x + 5 = 0? A. 0 B. 1 C. 2 D. 3 Answer: A
- The equation x^2 - 6x + 9 = 0 has a discriminant of: A. 72 B. 36 C. 0 D. -36 Answer: C
- y = x + k is a tangent to y = x^2 when k equals: A. 1/4 B. -1/4 C. 0 D. -1 Answer: B
Akwai a cikin manhajar Green Bridge
Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.
Akwai a cikin manhajar Green Bridge
Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.
Littattafan da ake ba da shawarar karantawa
Yi Aikin Tambayoyin Gwaji
Kana son yin aikin tambayoyin gwaji kan The Discriminant? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.
Sauke Manhajar Daga Google Playstore
Duk abin da kake buƙata don yin fice a JAMB, WAEC & NECO.
