Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9-8*x=-9*x+15
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Equation 4^x-1/2-6*2^x-1+3=0
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Equation x^2-25=0
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Equation x^2+6*x+7=0
- Express {x} in terms of y where:
- -16*x-9*y=-1
- -15*x+7*y=1
- 18*x-6*y=7
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Identical expressions
- k^ two - two *k- eight = zero
- k squared minus 2 multiply by k minus 8 equally 0
- k to the power of two minus two multiply by k minus eight equally zero
- k2-2*k-8=0
- k²-2*k-8=0
- k to the power of 2-2*k-8=0
- k^2-2k-8=0
- k2-2k-8=0
- k^2-2*k-8=O
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Similar expressions
- k^2+2*k-8=0
- k^2-2*k+8=0
k^2-2*k-8=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
$$a = 1$$
$$b = -2$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$k_{1} = 4$$
Simplify
$$k_{2} = -2$$
Simplify
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
$$a = 1$$
$$b = -2$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-8) = 36
Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 4$$
Simplify
$$k_{2} = -2$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 2$$
$$k_{1} k_{2} = -8$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 2$$
$$k_{1} k_{2} = -8$$
Sum and product of roots
[src]
sum
0 - 2 + 4
$$\left(-2 + 0\right) + 4$$
=
2
$$2$$
product
1*-2*4
$$1 \left(-2\right) 4$$
=
-8
$$-8$$
-8
The graph