ROOTS OF QUADRATIC EQUATION / AKAR PERSAMAAN KUADRAT

Input value of Coefficient of

x^{2}

$x^2$ , Coefficient of

x

$x$ and constant.
Masukkan koefisien

x^{2}

$x^2$ , koefisien

x

$x$ dan konstanta.

Roots of Quadratic Equation Calculator.

Kalkulator Akar Persamaan Kuadrat.

Let

a x^{2} + b x + c = 0

$ax^2+bx+c=0$ be a quadratic equation. The roots is given by:
Dari persamaan kuadrat

a x^{2} + b x + c = 0

$ax^2+bx+c=0$ , maka rumus untuk mencari akar-akarnya adalah:

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For Example / Contoh:
Find the roots of the quadratic equation

2 x^{2} - 3 x - 9 = 0

$2x^2-3x-9=0$ .
Carilah akar-akar dari persamaan kuadrat

2 x^{2} - 3 x - 9 = 0

$2x^2-3x-9=0$ !

Solution / Jawaban:

a = 2

$a=2$

b = - 3

$b=-3$

c = - 9

$c=-9$

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

= \frac{- (- 3) \pm \sqrt{(- 3)^{2} - 4.2. (- 9)}}{2.2}

$=\frac{-(-3)\pm \sqrt{(-3)^2-4.2.(-9)}}{2.2}$

= \frac{3 \pm \sqrt{9 + 72}}{4}

$=\frac{3\pm \sqrt{9+72}}{4}$

= \frac{3 \pm \sqrt{81}}{4}

$=\frac{3\pm \sqrt{81}}{4}$

= \frac{3 \pm 9}{4}

$=\frac{3\pm 9}{4}$

x_{1} = \frac{3 + 9}{4} = \frac{12}{4} = 3

$x_1=\frac{3+9}{4}=\frac{12}{4}=3$

x_{2} = \frac{3 - 9}{4} = \frac{- 6}{4} = - 1.5

$x_2=\frac{3-9}{4}=\frac{-6}{4}=-1.5$

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