Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3=27
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Equation x^4+2*x^2-8=0
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Equation cos(x)=2/3
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Equation (x-11)^4=(x+3)^4
- Express {x} in terms of y where:
- 6*x+17*y=3
- 1*x+4*y=20
- 20*x+7*y=-9
- -17*x+18*y=10
- Factor polynomial:
- x^2-6*x+5
- Factor squared:
- x^2-6*x+5
-
Identical expressions
- x^ two - six *x+ five = zero
- x squared minus 6 multiply by x plus 5 equally 0
- x to the power of two minus six multiply by x plus five equally zero
- x2-6*x+5=0
- x²-6*x+5=0
- x to the power of 2-6*x+5=0
- x^2-6x+5=0
- x2-6x+5=0
- x^2-6*x+5=O
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Similar expressions
- x^2+6*x+5=0
- x^2-6*x-5=0
- 7x^2-6x+5=0
x^2-6*x+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
$$a = 1$$
$$b = -6$$
$$c = 5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = 1$$
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
$$a = 1$$
$$b = -6$$
$$c = 5$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (5) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = 1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = 5$$
The graph