f(x)=3x^2-15x+9 eching

$$f ( x ) = 3 x ^ { 2 } - 15 x + 9$$

Omil

$$3\left(x-\frac{5-\sqrt{13}}{2}\right)\left(x-\frac{\sqrt{13}+5}{2}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$3x^{2}-15x+9=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 3\times 9}}{2\times 3}$$

-15 kvadratini chiqarish.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 3\times 9}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225-12\times 9}}{2\times 3}$$

-12 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225-108}}{2\times 3}$$

225 ni -108 ga qo'shish.

$$x=\frac{-\left(-15\right)±\sqrt{117}}{2\times 3}$$

117 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±3\sqrt{13}}{2\times 3}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±3\sqrt{13}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{15±3\sqrt{13}}{6}$$

x=\frac{15±3\sqrt{13}}{6} tenglamasini yeching, bunda ± musbat. 15 ni 3\sqrt{13} ga qo'shish.

$$x=\frac{3\sqrt{13}+15}{6}$$

15+3\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{\sqrt{13}+5}{2}$$

x=\frac{15±3\sqrt{13}}{6} tenglamasini yeching, bunda ± manfiy. 15 dan 3\sqrt{13} ni ayirish.

$$x=\frac{15-3\sqrt{13}}{6}$$

15-3\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{5-\sqrt{13}}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5+\sqrt{13}}{2} ga va x_{2} uchun \frac{5-\sqrt{13}}{2} ga bo‘ling.

$$3x^{2}-15x+9=3\left(x-\frac{\sqrt{13}+5}{2}\right)\left(x-\frac{5-\sqrt{13}}{2}\right)$$

Baholash

$$3\left(x^{2}-5x+3\right)$$