Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-5x=0
-
Equation sqrt(3)/2*cos(x)-1/2*sin(x)=1
-
Equation sin(x)=-0.5
-
Equation cos2x+5sinx+2=0
- Express {x} in terms of y where:
- 4*x+13*y=13
- -12*x+3*y=-9
- 17*x-19*y=1
- -1*x+19*y=-10
- Integral of d{x}:
-
x^2-5x
- Graphing y =:
- x^2-5x
- Derivative of:
-
x^2-5x
-
Identical expressions
- x^ two -5x= zero
- x squared minus 5x equally 0
- x to the power of two minus 5x equally zero
- x2-5x=0
- x²-5x=0
- x to the power of 2-5x=0
- x^2-5x=O
-
Similar expressions
- x^2+5x=0
x^2-5x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a*x^2 + b*x + c = 0$$
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = 0$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 0 + \left(-5\right)^{2} = 25$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 0$$
Simplify
$$a*x^2 + b*x + c = 0$$
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = 0$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 0 + \left(-5\right)^{2} = 25$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 0$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
0 + 5
$$\left(0\right) + \left(5\right)$$
=
5
$$5$$
product
0 * 5
$$\left(0\right) * \left(5\right)$$
=
0
$$0$$
The graph