Foirmle ceàrnanach
Tha am foirmle ceàrnanach air a chleachdadh nuair a bhios sinn a’ fuasgladh ceàrnanach nach gabh fhactaradh.
Seo am foirmle ceàrnanach:
\(x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\)
far a bheil a, b agus c gan toirt bho:
\(a{x^2} + bx + c\)
Eisimpleir
Fuasgail \(2{x^2} - 5x - 6 = 0\)
Freagairt
Bho nach gabh an ceàrnanach seo fhactaradh, cleachd am foirmle ceàrnanach, far a bheil a = 2, b = -5 agus c = -6.
\(x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\)
\(x = \frac{{ - ( - 5) \pm \sqrt {{{( - 5)}^2} - (4 \times 2 \times ( - 6))} }}{{2 \times 2}}\)
\(x = \frac{{5 \pm \sqrt {25 - ( - 48)} }}{4}\)
\(x = \frac{{5 \pm \sqrt {25 + 48} }}{4}\)
\(x = \frac{{5 \pm \sqrt {73} }}{4}\)
Bidh sinn a' briseadh seo ann an dà obrachadh
\(x = \frac{{5 + \sqrt {73} }}{4}\)
\(x=\frac{13.544}{4}\)
\(x = 3.39\,(gu\,2\,id)\)
Agus:
\(x = \frac{{5 - \sqrt {73} }}{4}\)
\(x=\frac{-3.544}{4}\)
\(x = - 0.89\,(gu\,2\,id)\)
Mar sin \(x = 3.39\,agus\,x = - 0.89\)
(Obraichidh am foirmle ceàrnanach airson co-aontar ceàrnanach sam bith – fiù 's ged a ghabhadh fhactaradh. Ach mar as trice, tha e nas luaithe factaradh a chleachdadh, ma ghabhas.)
Feuch a-nis a' cheist gu h-ìosal.
Question
Fuasgail \(3{x^2} + 7x + 4 = 0\)
a = 3, b = 7 agus c = 4
\(x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\)
\(x = \frac{{ - 7 \pm \sqrt {{7^2} - (4 \times 3 \times 4)} }}{{2 \times 3}}\)
\(x = \frac{{ - 7 \pm \sqrt {49 - (48)} }}{6}\)
\(x = \frac{{ - 7 \pm \sqrt 1 }}{6}\)
\(x = \frac{{ - 7 + \sqrt 1 }}{6}\)
\(x=\frac{-6}{6}\)
\(x=-1\)
Agus:
\(x = \frac{{ - 7 - \sqrt 1 }}{6}\)
\(x = - 1.33\,(gu\,2\,id)\)
Mar sin \(x = - 1\,agus\,x = - 1.33\)