Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation tan(x)=-1/2
-
Equation 1*(x-1)*(x-3)=0
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Equation 5x+12=8x+30
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Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- -2*x-19*y=3
- -2*x+18*y=13
- -2*x-15*y=-1
- 10*x-2*y=11
- Derivative of:
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5*x^2
- Limit of the function:
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5*x^2
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Identical expressions
- five *x^ two = zero
- 5 multiply by x squared equally 0
- five multiply by x to the power of two equally zero
- 5*x2=0
- 5*x²=0
- 5*x to the power of 2=0
- 5x^2=0
- 5x2=0
- 5*x^2=O
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Similar expressions
- x^3+5x^2+14x=0
- x^3+5*x^2-16x-80=0
- 5x^2+3x+6=0
5*x^2=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
$$a = 5$$
$$b = 0$$
$$c = 0$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 0$$
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
$$a = 5$$
$$b = 0$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (5) * (0) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -0/2/(5)
$$x_{1} = 0$$
Vieta's Theorem
rewrite the equation
$$5 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 0$$
$$5 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 0$$
The graph