Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+12=5
-
Equation 3/(x-5)+8/x=2
-
Equation (5x-2)*(-x+3)=0
-
Equation 1-x/2=x/3
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- -7*x-13*y=-12
- Graphing y =:
- x^2-8*x+16
- Factor squared:
- x^2-8*x+16
- Factor polynomial:
- x^2-8*x+16
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Identical expressions
- x^ two - eight *x+ sixteen = zero
- x squared minus 8 multiply by x plus 16 equally 0
- x to the power of two minus eight multiply by x plus sixteen equally zero
- x2-8*x+16=0
- x²-8*x+16=0
- x to the power of 2-8*x+16=0
- x^2-8x+16=0
- x2-8x+16=0
- x^2-8*x+16=O
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Similar expressions
- x^2-8*x-16=0
- x^2+8*x+16=0
x^2-8*x+16=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
$$a = 1$$
$$b = -8$$
$$c = 16$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 4$$
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
$$a = 1$$
$$b = -8$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (16) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --8/2/(1)
$$x_{1} = 4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 16$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 16$$
The graph