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- Equation:
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Equation x^2-12x+36=0
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Equation 8x^2=0
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- Express {x} in terms of y where:
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- Graphing y =:
- x^2-12x+36
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Identical expressions
- x^ two -12x+ thirty-six = zero
- x squared minus 12x plus 36 equally 0
- x to the power of two minus 12x plus thirty minus six equally zero
- x2-12x+36=0
- x²-12x+36=0
- x to the power of 2-12x+36=0
- x^2-12x+36=O
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Similar expressions
- x^2+12x+36=0
- x^2-12x-36=0
x^2-12x+36=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -12$$
$$c = 36$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 36 + \left(-12\right)^{2} = 0$$
Because D = 0, then the equation has one root.
$$x_{1} = 6$$
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -12$$
$$c = 36$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 36 + \left(-12\right)^{2} = 0$$
Because D = 0, then the equation has one root.
x = -b/2a = --12/2/(1)
$$x_{1} = 6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = 36$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = 36$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = 36$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = 36$$
Sum and product of roots
[src]
sum
6
$$\left(6\right)$$
=
6
$$6$$
product
6
$$\left(6\right)$$
=
6
$$6$$
The graph