Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4,3x-3,5=2,5x+1,9
-
Equation x^6=-64
-
Equation sin(x)=5/2
-
Equation (x+4)(x+2)-(x-0,5)(x+2)=0
- Express {x} in terms of y where:
- -8*x+5*y=-17
- -18*x-17*y=-5
- -13*x+5*y=15
- 13*x-7*y=8
- Derivative of:
- x^2+5x+1
-
Identical expressions
- x^ two +5x+ one = zero
- x squared plus 5x plus 1 equally 0
- x to the power of two plus 5x plus one equally zero
- x2+5x+1=0
- x²+5x+1=0
- x to the power of 2+5x+1=0
- x^2+5x+1=O
-
Similar expressions
- x^2-5x+1=0
- x^2+5x-1=0
x^2+5x+1=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
$$a = 1$$
$$b = 5$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{5}{2} + \frac{\sqrt{21}}{2}$$
$$x_{2} = - \frac{5}{2} - \frac{\sqrt{21}}{2}$$
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
$$a = 1$$
$$b = 5$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (1) * (1) = 21
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{5}{2} + \frac{\sqrt{21}}{2}$$
$$x_{2} = - \frac{5}{2} - \frac{\sqrt{21}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 5$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -5$$
$$x_{1} x_{2} = 1$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 5$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -5$$
$$x_{1} x_{2} = 1$$
Rapid solution
[src]
____
5 \/ 21
x1 = - - - ------
2 2
$$x_{1} = - \frac{5}{2} - \frac{\sqrt{21}}{2}$$
____
5 \/ 21
x2 = - - + ------
2 2
$$x_{2} = - \frac{5}{2} + \frac{\sqrt{21}}{2}$$
x2 = -5/2 + sqrt(21)/2
Sum and product of roots
[src]
sum
____ ____ 5 \/ 21 5 \/ 21 - - - ------ + - - + ------ 2 2 2 2
$$\left(- \frac{5}{2} - \frac{\sqrt{21}}{2}\right) + \left(- \frac{5}{2} + \frac{\sqrt{21}}{2}\right)$$
=
-5
$$-5$$
product
/ ____\ / ____\ | 5 \/ 21 | | 5 \/ 21 | |- - - ------|*|- - + ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{5}{2} - \frac{\sqrt{21}}{2}\right) \left(- \frac{5}{2} + \frac{\sqrt{21}}{2}\right)$$
=
1
$$1$$
1
The graph