Réitigh 3b^2+15b+2

$$3 b ^ { 2 } + 15 b + 2$$

Fachtóirigh

$$3\left(b-\left(-\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)\left(b-\left(\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)$$

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Is féidir an trasfhoirmiú ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) a úsáid chun luach iltéarmach cearnach a fhachtóiriú, nuair is réitigh iad x_{1} agus x_{2} ar an gcothromóid chearnach ax^{2}+bx+c=0.

$$3b^{2}+15b+2=0$$

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

$$b=\frac{-15±\sqrt{15^{2}-4\times 3\times 2}}{2\times 3}$$

Cearnóg 15.

$$b=\frac{-15±\sqrt{225-4\times 3\times 2}}{2\times 3}$$

Méadaigh -4 faoi 3.

$$b=\frac{-15±\sqrt{225-12\times 2}}{2\times 3}$$

Méadaigh -12 faoi 2.

$$b=\frac{-15±\sqrt{225-24}}{2\times 3}$$

Suimigh 225 le -24?

$$b=\frac{-15±\sqrt{201}}{2\times 3}$$

Méadaigh 2 faoi 3.

$$b=\frac{-15±\sqrt{201}}{6}$$

Réitigh an chothromóid b=\frac{-15±\sqrt{201}}{6} nuair is ionann ± agus plus. Suimigh -15 le \sqrt{201}?

$$b=\frac{\sqrt{201}-15}{6}$$

Roinn -15+\sqrt{201} faoi 6.

$$b=\frac{\sqrt{201}}{6}-\frac{5}{2}$$

Réitigh an chothromóid b=\frac{-15±\sqrt{201}}{6} nuair is ionann ± agus míneas. Dealaigh \sqrt{201} ó -15.

$$b=\frac{-\sqrt{201}-15}{6}$$

Roinn -15-\sqrt{201} faoi 6.

$$b=-\frac{\sqrt{201}}{6}-\frac{5}{2}$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir -\frac{5}{2}+\frac{\sqrt{201}}{6} in ionad x_{1} agus -\frac{5}{2}-\frac{\sqrt{201}}{6} in ionad x_{2}.

$$3b^{2}+15b+2=3\left(b-\left(\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)\left(b-\left(-\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)$$

Luacháil

$$3b^{2}+15b+2$$