f(x)=7x^2+x-1 eching

$$f ( x ) = 7 x ^ { 2 } + x - 1$$

Omil

$$7\left(x-\frac{-\sqrt{29}-1}{14}\right)\left(x-\frac{\sqrt{29}-1}{14}\right)$$

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.

$$7x^{2}+x-1=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 7\left(-1\right)}}{2\times 7}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\times 7\left(-1\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-28\left(-1\right)}}{2\times 7}$$

-28 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+28}}{2\times 7}$$

1 ni 28 ga qo'shish.

$$x=\frac{-1±\sqrt{29}}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{29}}{14}$$

x=\frac{-1±\sqrt{29}}{14} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{29} ga qo'shish.

$$x=\frac{\sqrt{29}-1}{14}$$

x=\frac{-1±\sqrt{29}}{14} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{29} ni ayirish.

$$x=\frac{-\sqrt{29}-1}{14}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-1+\sqrt{29}}{14} ga va x_{2} uchun \frac{-1-\sqrt{29}}{14} ga bo‘ling.

$$7x^{2}+x-1=7\left(x-\frac{\sqrt{29}-1}{14}\right)\left(x-\frac{-\sqrt{29}-1}{14}\right)$$

Baholash

$$7x^{2}+x-1$$