The Discriminant
Muhtasari
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.
Malengo
- 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.
Maelezo ya Somo
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Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Tathmini ya Somo
Hongera kwa kukamilisha somo la The Discriminant. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- 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
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Vitabu Vinavyopendekezwa
Fanya Mazoezi ya Maswali ya Majaribio
Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu The Discriminant? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.
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