4a^2-11a-5 eching

$$4 { a }^{ 2 } -11a-5$$

Omil

$$4\left(a-\frac{11-\sqrt{201}}{8}\right)\left(a-\frac{\sqrt{201}+11}{8}\right)$$

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.

$$4a^{2}-11a-5=0$$

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.

$$a=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 4\left(-5\right)}}{2\times 4}$$

-11 kvadratini chiqarish.

$$a=\frac{-\left(-11\right)±\sqrt{121-4\times 4\left(-5\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$a=\frac{-\left(-11\right)±\sqrt{121-16\left(-5\right)}}{2\times 4}$$

-16 ni -5 marotabaga ko'paytirish.

$$a=\frac{-\left(-11\right)±\sqrt{121+80}}{2\times 4}$$

121 ni 80 ga qo'shish.

$$a=\frac{-\left(-11\right)±\sqrt{201}}{2\times 4}$$

-11 ning teskarisi 11 ga teng.

$$a=\frac{11±\sqrt{201}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$a=\frac{11±\sqrt{201}}{8}$$

a=\frac{11±\sqrt{201}}{8} tenglamasini yeching, bunda ± musbat. 11 ni \sqrt{201} ga qo'shish.

$$a=\frac{\sqrt{201}+11}{8}$$

a=\frac{11±\sqrt{201}}{8} tenglamasini yeching, bunda ± manfiy. 11 dan \sqrt{201} ni ayirish.

$$a=\frac{11-\sqrt{201}}{8}$$

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{201}}{8} ga va x_{2} uchun \frac{11-\sqrt{201}}{8} ga bo‘ling.

$$4a^{2}-11a-5=4\left(a-\frac{\sqrt{201}+11}{8}\right)\left(a-\frac{11-\sqrt{201}}{8}\right)$$

Baholash

$$4a^{2}-11a-5$$