x^2+11x+3 eching

$$x ^ { 2 } + 11 x + 3$$

Omil

$$\left(x-\frac{-\sqrt{109}-11}{2}\right)\left(x-\frac{\sqrt{109}-11}{2}\right)$$

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.

$$x^{2}+11x+3=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 3}}{2}$$

11 kvadratini chiqarish.

$$x=\frac{-11±\sqrt{121-4\times 3}}{2}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121-12}}{2}$$

121 ni -12 ga qo'shish.

$$x=\frac{-11±\sqrt{109}}{2}$$

x=\frac{-11±\sqrt{109}}{2} tenglamasini yeching, bunda ± musbat. -11 ni \sqrt{109} ga qo'shish.

$$x=\frac{\sqrt{109}-11}{2}$$

x=\frac{-11±\sqrt{109}}{2} tenglamasini yeching, bunda ± manfiy. -11 dan \sqrt{109} ni ayirish.

$$x=\frac{-\sqrt{109}-11}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-11+\sqrt{109}}{2} ga va x_{2} uchun \frac{-11-\sqrt{109}}{2} ga bo‘ling.

$$x^{2}+11x+3=\left(x-\frac{\sqrt{109}-11}{2}\right)\left(x-\frac{-\sqrt{109}-11}{2}\right)$$

Baholash

$$x^{2}+11x+3$$