Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation k^2-5*k+6=0
- Equation x(y+1)2=243y
- Equation 121p²+14p+2=0
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Equation x^4-8x^2+16=0
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
- Graphing y =:
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k^2-5*k+6
- Sum of series:
- k^2-5*k+6
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Identical expressions
- k^ two - five *k+ six = zero
- k squared minus 5 multiply by k plus 6 equally 0
- k to the power of two minus five multiply by k plus six equally zero
- k2-5*k+6=0
- k²-5*k+6=0
- k to the power of 2-5*k+6=0
- k^2-5k+6=0
- k2-5k+6=0
- k^2-5*k+6=O
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Similar expressions
- k^2-5*k-6=0
- k^2+5*k+6=0
k^2-5*k+6=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:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$k_{1} = 3$$
$$k_{2} = 2$$
a*k^2 + b*k + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (6) = 1
Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 3$$
$$k_{2} = 2$$
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 5$$
$$k_{1} k_{2} = 6$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 5$$
$$k_{1} k_{2} = 6$$
The graph