Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x-4/3+x/2=5
-
Equation 7*x^2-28=0
- Equation |x-3|+|x+2|-|x-4|=3
- Equation 1/3x+20=1/13x-29
- Express {x} in terms of y where:
- -3*x+8*y=4
- 8*x+5*y=5
- 15*x+19*y=1
- -12*x+8*y=14
- Sum of series:
-
x²
- Derivative of:
-
x²
- Integral of d{x}:
-
x²
-
Identical expressions
- x²= one . twenty-five
- x² equally 1.25
- x² equally one . twenty minus five
x²=1.25 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} = \frac{5}{4}$$
to
$$x^{2} - \frac{5}{4} = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = - \frac{5}{4}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{5}}{2}$$
$$x_{2} = - \frac{\sqrt{5}}{2}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = \frac{5}{4}$$
to
$$x^{2} - \frac{5}{4} = 0$$
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 - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = - \frac{5}{4}$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-5/4) = 5
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{5}}{2}$$
$$x_{2} = - \frac{\sqrt{5}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{5}{4}$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{5}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{5}{4}$$
Rapid solution
[src]
___
-\/ 5
x1 = -------
2
$$x_{1} = - \frac{\sqrt{5}}{2}$$
___
\/ 5
x2 = -----
2
$$x_{2} = \frac{\sqrt{5}}{2}$$
x2 = sqrt(5)/2
Sum and product of roots
[src]
sum
___ ___
\/ 5 \/ 5
- ----- + -----
2 2
$$- \frac{\sqrt{5}}{2} + \frac{\sqrt{5}}{2}$$
=
0
$$0$$
product
___ ___ -\/ 5 \/ 5 -------*----- 2 2
$$- \frac{\sqrt{5}}{2} \frac{\sqrt{5}}{2}$$
=
-5/4
$$- \frac{5}{4}$$
-5/4