Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 4-6*(x+2)=3-5*x
-
Equation 4-6(x+2)=3-5x
-
Equation 1+sin(x)=0
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Equation x^2-3*x+1=0
- Express {x} in terms of y where:
- 18*x-8*y=-2
- -11*x+15*y=7
- 6*x+17*y=3
- 1*x+10*y=-18
- Graphing y =:
- x^2-3*x+1
- Factor squared:
- x^2-3*x+1
- Factor polynomial:
- x^2-3*x+1
-
Identical expressions
- x^ two - three *x+ one = zero
- x squared minus 3 multiply by x plus 1 equally 0
- x to the power of two minus three multiply by x plus one equally zero
- x2-3*x+1=0
- x²-3*x+1=0
- x to the power of 2-3*x+1=0
- x^2-3x+1=0
- x2-3x+1=0
- x^2-3*x+1=O
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Similar expressions
- x^2-3*x-1=0
- x^2+3*x+1=0
x^2-3*x+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
$$a = 1$$
$$b = -3$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{5}}{2} + \frac{3}{2}$$
$$x_{2} = \frac{3}{2} - \frac{\sqrt{5}}{2}$$
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
$$a = 1$$
$$b = -3$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (1) * (1) = 5
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{5}}{2} + \frac{3}{2}$$
$$x_{2} = \frac{3}{2} - \frac{\sqrt{5}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 1$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 1$$
Rapid solution
[src]
___
3 \/ 5
x1 = - - -----
2 2
$$x_{1} = \frac{3}{2} - \frac{\sqrt{5}}{2}$$
___
3 \/ 5
x2 = - + -----
2 2
$$x_{2} = \frac{\sqrt{5}}{2} + \frac{3}{2}$$
x2 = sqrt(5)/2 + 3/2
Sum and product of roots
[src]
sum
___ ___ 3 \/ 5 3 \/ 5 - - ----- + - + ----- 2 2 2 2
$$\left(\frac{3}{2} - \frac{\sqrt{5}}{2}\right) + \left(\frac{\sqrt{5}}{2} + \frac{3}{2}\right)$$
=
3
$$3$$
product
/ ___\ / ___\ |3 \/ 5 | |3 \/ 5 | |- - -----|*|- + -----| \2 2 / \2 2 /
$$\left(\frac{3}{2} - \frac{\sqrt{5}}{2}\right) \left(\frac{\sqrt{5}}{2} + \frac{3}{2}\right)$$
=
1
$$1$$
1
The graph