Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (-5*x-3)*(2*x-1)=0
- Equation x^2-1=1+(1/2)*y
-
Equation 5-2(x-1)=4-x
-
Equation x^2+x-4=0
- Express {x} in terms of y where:
- -10*x+16*y=-6
- -11*x-14*y=-3
- 4*x-1*y=-3
- -10*x-18*y=15
- Factor squared:
- x^2+x-4
- Factor polynomial:
- x^2+x-4
-
Identical expressions
- x^ two +x- four = zero
- x squared plus x minus 4 equally 0
- x to the power of two plus x minus four equally zero
- x2+x-4=0
- x²+x-4=0
- x to the power of 2+x-4=0
- x^2+x-4=O
-
Similar expressions
- x^2+x+4=0
- x^2-x-4=0
x^2+x-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
$$a = 1$$
$$b = 1$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{17}}{2}$$
$$x_{2} = - \frac{\sqrt{17}}{2} - \frac{1}{2}$$
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
$$a = 1$$
$$b = 1$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-4) = 17
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{17}}{2}$$
$$x_{2} = - \frac{\sqrt{17}}{2} - \frac{1}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -4$$
Rapid solution
[src]
____
1 \/ 17
x1 = - - + ------
2 2
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{17}}{2}$$
____
1 \/ 17
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{17}}{2} - \frac{1}{2}$$
x2 = -sqrt(17)/2 - 1/2
Sum and product of roots
[src]
sum
____ ____ 1 \/ 17 1 \/ 17 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{17}}{2} - \frac{1}{2}\right) + \left(- \frac{1}{2} + \frac{\sqrt{17}}{2}\right)$$
=
-1
$$-1$$
product
/ ____\ / ____\ | 1 \/ 17 | | 1 \/ 17 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{1}{2} + \frac{\sqrt{17}}{2}\right) \left(- \frac{\sqrt{17}}{2} - \frac{1}{2}\right)$$
=
-4
$$-4$$
-4
The graph