Réitigh 3k^2+6k-4

$$3 k ^ { 2 } + 6 k - 4$$

Fachtóirigh

$$3\left(k-\left(-\frac{\sqrt{21}}{3}-1\right)\right)\left(k-\left(\frac{\sqrt{21}}{3}-1\right)\right)$$

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.

$$3k^{2}+6k-4=0$$

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.

$$k=\frac{-6±\sqrt{6^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Cearnóg 6.

$$k=\frac{-6±\sqrt{36-4\times 3\left(-4\right)}}{2\times 3}$$

Méadaigh -4 faoi 3.

$$k=\frac{-6±\sqrt{36-12\left(-4\right)}}{2\times 3}$$

Méadaigh -12 faoi -4.

$$k=\frac{-6±\sqrt{36+48}}{2\times 3}$$

Suimigh 36 le 48?

$$k=\frac{-6±\sqrt{84}}{2\times 3}$$

Tóg fréamh chearnach 84.

$$k=\frac{-6±2\sqrt{21}}{2\times 3}$$

Méadaigh 2 faoi 3.

$$k=\frac{-6±2\sqrt{21}}{6}$$

Réitigh an chothromóid k=\frac{-6±2\sqrt{21}}{6} nuair is ionann ± agus plus. Suimigh -6 le 2\sqrt{21}?

$$k=\frac{2\sqrt{21}-6}{6}$$

Roinn -6+2\sqrt{21} faoi 6.

$$k=\frac{\sqrt{21}}{3}-1$$

Réitigh an chothromóid k=\frac{-6±2\sqrt{21}}{6} nuair is ionann ± agus míneas. Dealaigh 2\sqrt{21} ó -6.

$$k=\frac{-2\sqrt{21}-6}{6}$$

Roinn -6-2\sqrt{21} faoi 6.

$$k=-\frac{\sqrt{21}}{3}-1$$

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir -1+\frac{\sqrt{21}}{3} in ionad x_{1} agus -1-\frac{\sqrt{21}}{3} in ionad x_{2}.

$$3k^{2}+6k-4=3\left(k-\left(\frac{\sqrt{21}}{3}-1\right)\right)\left(k-\left(-\frac{\sqrt{21}}{3}-1\right)\right)$$

Luacháil

$$3k^{2}+6k-4$$