Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x/12+x=55/12
-
Equation x^2-2x+5=0
-
Equation cos(x)=2/3
-
Equation 4x+1=-3x+15
- Express {x} in terms of y where:
- -4*x+6*y=-7
- 2*x+3*y=14
- 18*x-8*y=-2
- 10*x-16*y=-6
- Graphing y =:
- x^2+4x-5
- Canonical form:
- x^2+4x-5
-
Identical expressions
- x^ two +4x- five = zero
- x squared plus 4x minus 5 equally 0
- x to the power of two plus 4x minus five equally zero
- x2+4x-5=0
- x²+4x-5=0
- x to the power of 2+4x-5=0
- x^2+4x-5=O
-
Similar expressions
- x^2+4x+5=0
- x^2-4x-5=0
x^2+4x-5=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
$$a = 1$$
$$b = 4$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = -5$$
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
$$a = 1$$
$$b = 4$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (-5) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -5$$
The graph