4x^2-15x-24 eching

$$4 x ^ { 2 } - 15 x - 24$$

Omil

$$4\left(x-\frac{15-\sqrt{609}}{8}\right)\left(x-\frac{\sqrt{609}+15}{8}\right)$$

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.

$$4x^{2}-15x-24=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 4\left(-24\right)}}{2\times 4}$$

-15 kvadratini chiqarish.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 4\left(-24\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225-16\left(-24\right)}}{2\times 4}$$

-16 ni -24 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225+384}}{2\times 4}$$

225 ni 384 ga qo'shish.

$$x=\frac{-\left(-15\right)±\sqrt{609}}{2\times 4}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±\sqrt{609}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{15±\sqrt{609}}{8}$$

x=\frac{15±\sqrt{609}}{8} tenglamasini yeching, bunda ± musbat. 15 ni \sqrt{609} ga qo'shish.

$$x=\frac{\sqrt{609}+15}{8}$$

x=\frac{15±\sqrt{609}}{8} tenglamasini yeching, bunda ± manfiy. 15 dan \sqrt{609} ni ayirish.

$$x=\frac{15-\sqrt{609}}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{15+\sqrt{609}}{8} ga va x_{2} uchun \frac{15-\sqrt{609}}{8} ga bo‘ling.

$$4x^{2}-15x-24=4\left(x-\frac{\sqrt{609}+15}{8}\right)\left(x-\frac{15-\sqrt{609}}{8}\right)$$

Baholash

$$4x^{2}-15x-24$$