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
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Equation 2x^2-x-1=x^2-5x-(-1-x^2)
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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 polynomial:
- 2*x^2-8*x
-
Identical expressions
- two *x^ two - eight *x= zero
- 2 multiply by x squared minus 8 multiply by x equally 0
- two multiply by x to the power of two minus eight multiply by x equally zero
- 2*x2-8*x=0
- 2*x²-8*x=0
- 2*x to the power of 2-8*x=0
- 2x^2-8x=0
- 2x2-8x=0
- 2*x^2-8*x=O
-
Similar expressions
- 2*x^2+8*x=0
2*x^2-8*x=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
$$a = 2$$
$$b = -8$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = 0$$
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
$$a = 2$$
$$b = -8$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (2) * (0) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = 0$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} - 8 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 0$$
$$2 x^{2} - 8 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 0$$
The graph