f(x)=-125x^2+1375x-1500 eching

$$f ( x ) = - 125 x ^ { 2 } + 1375 x - 1500$$

Omil

$$-125\left(x-\frac{11-\sqrt{73}}{2}\right)\left(x-\frac{\sqrt{73}+11}{2}\right)$$

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.

$$-125x^{2}+1375x-1500=0$$

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.

$$x=\frac{-1375±\sqrt{1375^{2}-4\left(-125\right)\left(-1500\right)}}{2\left(-125\right)}$$

1375 kvadratini chiqarish.

$$x=\frac{-1375±\sqrt{1890625-4\left(-125\right)\left(-1500\right)}}{2\left(-125\right)}$$

-4 ni -125 marotabaga ko'paytirish.

$$x=\frac{-1375±\sqrt{1890625+500\left(-1500\right)}}{2\left(-125\right)}$$

500 ni -1500 marotabaga ko'paytirish.

$$x=\frac{-1375±\sqrt{1890625-750000}}{2\left(-125\right)}$$

1890625 ni -750000 ga qo'shish.

$$x=\frac{-1375±\sqrt{1140625}}{2\left(-125\right)}$$

1140625 ning kvadrat ildizini chiqarish.

$$x=\frac{-1375±125\sqrt{73}}{2\left(-125\right)}$$

2 ni -125 marotabaga ko'paytirish.

$$x=\frac{-1375±125\sqrt{73}}{-250}$$

x=\frac{-1375±125\sqrt{73}}{-250} tenglamasini yeching, bunda ± musbat. -1375 ni 125\sqrt{73} ga qo'shish.

$$x=\frac{125\sqrt{73}-1375}{-250}$$

-1375+125\sqrt{73} ni -250 ga bo'lish.

$$x=\frac{11-\sqrt{73}}{2}$$

x=\frac{-1375±125\sqrt{73}}{-250} tenglamasini yeching, bunda ± manfiy. -1375 dan 125\sqrt{73} ni ayirish.

$$x=\frac{-125\sqrt{73}-1375}{-250}$$

-1375-125\sqrt{73} ni -250 ga bo'lish.

$$x=\frac{\sqrt{73}+11}{2}$$

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{73}}{2} ga va x_{2} uchun \frac{11+\sqrt{73}}{2} ga bo‘ling.

$$-125x^{2}+1375x-1500=-125\left(x-\frac{11-\sqrt{73}}{2}\right)\left(x-\frac{\sqrt{73}+11}{2}\right)$$

Baholash

$$-125x^{2}+1375x-1500$$