Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5^x=125
-
Equation -x=2
-
Equation -2*x-4=3*x
- Equation x+y=4
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 18*x+20*y=-2
- -5*x-6*y=-1
- 4*x+12*y=-11
- Graphing y =:
- 5*x^2-4
- Factor polynomial:
- 5*x^2-4
-
Identical expressions
- five *x^ two - four = zero
- 5 multiply by x squared minus 4 equally 0
- five multiply by x to the power of two minus four equally zero
- 5*x2-4=0
- 5*x²-4=0
- 5*x to the power of 2-4=0
- 5x^2-4=0
- 5x2-4=0
- 5*x^2-4=O
-
Similar expressions
- 5*x^2+4=0
5*x^2-4=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
$$a = 5$$
$$b = 0$$
$$c = -4$$
, then
$$D = b^2 - 4 * a * c = $$
$$0^{2} - 5 \cdot 4 \left(-4\right) = 80$$
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
$$x_{1} = \frac{2 \sqrt{5}}{5}$$
Simplify
$$x_{2} = - \frac{2 \sqrt{5}}{5}$$
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
$$a = 5$$
$$b = 0$$
$$c = -4$$
, then
$$D = b^2 - 4 * a * c = $$
$$0^{2} - 5 \cdot 4 \left(-4\right) = 80$$
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
$$x_{1} = \frac{2 \sqrt{5}}{5}$$
Simplify
$$x_{2} = - \frac{2 \sqrt{5}}{5}$$
Simplify
Vieta's Theorem
rewrite the equation
$$5 x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{4}{5} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{4}{5}$$
$$5 x^{2} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{4}{5} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{4}{5}$$
Sum and product of roots
[src]
sum
___ ___ -2*\/ 5 2*\/ 5 -------- + ------- 5 5
$$\left(- \frac{2 \sqrt{5}}{5}\right) + \left(\frac{2 \sqrt{5}}{5}\right)$$
=
0
$$0$$
product
___ ___ -2*\/ 5 2*\/ 5 -------- * ------- 5 5
$$\left(- \frac{2 \sqrt{5}}{5}\right) * \left(\frac{2 \sqrt{5}}{5}\right)$$
=
-4/5
$$- \frac{4}{5}$$
Rapid solution
[src]
___
-2*\/ 5
x_1 = --------
5
$$x_{1} = - \frac{2 \sqrt{5}}{5}$$
___
2*\/ 5
x_2 = -------
5
$$x_{2} = \frac{2 \sqrt{5}}{5}$$
The graph