Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-9x+20=0
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Equation k^2-6*k+9=0
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Equation x^4=625
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Equation 8x^2=0
- Express {x} in terms of y where:
- 4*x-16*y=6
- 10*x-1*y=10
- 15*x-17*y=19
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
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Identical expressions
- k^ two - six *k+ nine = zero
- k squared minus 6 multiply by k plus 9 equally 0
- k to the power of two minus six multiply by k plus nine equally zero
- k2-6*k+9=0
- k²-6*k+9=0
- k to the power of 2-6*k+9=0
- k^2-6k+9=0
- k2-6k+9=0
- k^2-6*k+9=O
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Similar expressions
- k^2-6*k-9=0
- k^2+6*k+9=0
k^2-6*k+9=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
$$a = 1$$
$$b = -6$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$k_{1} = 3$$
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
$$a = 1$$
$$b = -6$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (9) = 0
Because D = 0, then the equation has one root.
k = -b/2a = --6/2/(1)
$$k_{1} = 3$$
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 6$$
$$k_{1} k_{2} = 9$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 6$$
$$k_{1} k_{2} = 9$$
The graph