Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 25*x^3-10*x^2+x=0
-
Equation 2x^2-x-1=x^2-5x-(-1-x^2)
-
Equation 2^x=5
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Equation (x-10)^2=(x+4)^2
- Express {x} in terms of y where:
- 15*x+12*y=-19
- -19*x-20*y=-4
- -18*x+12*y=-8
- -14*x+4*y=-16
- Factor squared:
- x^2+8*x+16
-
Identical expressions
- x^ two + eight *x+ sixteen = zero
- x squared plus 8 multiply by x plus 16 equally 0
- x to the power of two plus 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