Te whakaoti whārite pūrua

Whārite tapawhā he whārite pāngarau, e pēnei ana te āhua:

ax² + bx + c = 0

Koinei te raupapa tuarua o te polynomial me te 3 whakarea:

• a – whakarea matua (tuatahi), kaua e rite ki te 0;
• b – tauwaenga (tuarua) whakarea;
• c he huānga kore utu.

Ko te otinga o te whārite tapawhā ko te kimi i ngā tau e rua (ōna pūtake) – x₁ me te x₂.

Te tātai mō te tātai i ngā pakiaka

Hei kimi i nga putake o te wharite tapawha, ka whakamahia te tauira:

Ko te kupu i roto i te pakiaka tapawha ka kiia whakahāwea a kua tohua ki te reta D (Δ ranei):

D = b² - 4ac

I tenei ara, Ko te tauira mo te tatau i nga pakiaka ka taea te whakaatu i nga huarahi rereke:

1 D > 0, e 2 ngā pūtake o te whārite:

2 D = 0, kotahi anake te pūtake o te whārite:

3 D < 0, вещественных корней нет, но есть комплексные:

Nga otinga o nga whārite tapawhā

tauira 1

3x² + 5x +2 = 0

Te whakatau:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

tauira 2

3x² - 6x +3 = 0

Te whakatau:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

tauira 3

x² + 2x +5 = 0

Te whakatau:

a = 1, b = 2, c = 5

I tenei keehi, karekau he tino putake, he tau uaua te otinga:

x₁ = -1 + 2i

x₂ = -1 – 2i

Kauwhata o te mahi tapawhā

Ko te kauwhata o te mahi tapawhā ko he kupu whakarite.

f(x) = ax² + b x + c

• Ko nga putake o te wharite tapawha ko nga pito o te mokowhititanga o te parapara me te tuaka abscissa (X).
• Mena kotahi anake te pakiaka, ka pa te parapara ki te tuaka i tetahi waahi kaore e whakawhiti.
• Ki te kore he tino putake (te aroaro o nga mea uaua), he kauwhata whai tuaka X e kore e pa.