Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x+y=3
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Equation x^2-5x+4=0
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Equation 9-4x=3x-40
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Equation x^2=8
- Express {x} in terms of y where:
- -17*x+18*y=10
- 18*x+12*y=18
- -11*x-3*y=14
- -20*x-13*y=15
- Integral of d{x}:
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x^2-5x+4
- Graphing y =:
-
x^2-5x+4
- Derivative of:
-
x^2-5x+4
-
Identical expressions
- x^ two -5x+ four = zero
- x squared minus 5x plus 4 equally 0
- x to the power of two minus 5x plus four equally zero
- x2-5x+4=0
- x²-5x+4=0
- x to the power of 2-5x+4=0
- x^2-5x+4=O
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Similar expressions
- x^2+5x+4=0
- x^2-5x-4=0
x^2-5x+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
$$a = 1$$
$$b = -5$$
$$c = 4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = 1$$
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
$$a = 1$$
$$b = -5$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (4) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = 1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 4$$
The graph