Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^6=(3x-2)^3
-
Equation 2x^2+5x-2=0
-
Equation 1/4*x^2-4=0
-
Equation x^2-10x=0
- Express {x} in terms of y where:
- -14*x+12*y=-6
- -10*x+8*y=2
- -16*x+1*y=-14
- 4*x-1*y=12
-
Identical expressions
- one / four *x^ two - four = zero
- 1 divide by 4 multiply by x squared minus 4 equally 0
- one divide by four multiply by x to the power of two minus four equally zero
- 1/4*x2-4=0
- 1/4*x²-4=0
- 1/4*x to the power of 2-4=0
- 1/4x^2-4=0
- 1/4x2-4=0
- 1/4*x^2-4=O
- 1 divide by 4*x^2-4=0
-
Similar expressions
- 1/4*x^2+4=0
1/4*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 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 - it is the discriminant.
Because
$$a = \frac{1}{4}$$
$$b = 0$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -4$$
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 - it is the discriminant.
Because
$$a = \frac{1}{4}$$
$$b = 0$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1/4) * (-4) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -4$$
Vieta's Theorem
rewrite the equation
$$\frac{x^{2}}{4} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -16$$
$$\frac{x^{2}}{4} - 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -16$$
Sum and product of roots
[src]
sum
-4 + 4
$$-4 + 4$$
=
0
$$0$$
product
-4*4
$$- 16$$
=
-16
$$-16$$
-16
The graph