Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x/4+13=x+1
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Equation 2x^2-x-1=x^2-5x-(-1-x^2)
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Equation x^3-x^2-x-1=0
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Equation -x=3
- Express {x} in terms of y where:
- 10*x-2*y=11
- -18*x-14*y=12
- 13*x-18*y=-17
- 4*x+18*y=-7
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Identical expressions
- sqrt(two *x+ three -x^ two)= zero
- square root of (2 multiply by x plus 3 minus x squared ) equally 0
- square root of (two multiply by x plus three minus x to the power of two) equally zero
- √(2*x+3-x^2)=0
- sqrt(2*x+3-x2)=0
- sqrt2*x+3-x2=0
- sqrt(2*x+3-x²)=0
- sqrt(2*x+3-x to the power of 2)=0
- sqrt(2x+3-x^2)=0
- sqrt(2x+3-x2)=0
- sqrt2x+3-x2=0
- sqrt2x+3-x^2=0
- sqrt(2*x+3-x^2)=O
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Similar expressions
- sqrt(2*x-3-x^2)=0
- sqrt(2*x+3+x^2)=0
sqrt(2*x+3-x^2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
$$\sqrt{- x^{2} + 2 x + 3} + 0 = 0$$
transform
$$- x^{2} + 2 x + 3 = 0$$
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
$$a = -1$$
$$b = 2$$
$$c = 3$$
, then
$$D = b^2 - 4 * a * c = $$
$$2^{2} - \left(-1\right) 4 \cdot 3 = 16$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = -1$$
Simplify
$$x_{2} = 3$$
Simplify
transform
$$- x^{2} + 2 x + 3 = 0$$
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
$$a = -1$$
$$b = 2$$
$$c = 3$$
, then
$$D = b^2 - 4 * a * c = $$
$$2^{2} - \left(-1\right) 4 \cdot 3 = 16$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = -1$$
Simplify
$$x_{2} = 3$$
Simplify
Sum and product of roots
[src]
sum
-1 + 3
$$\left(-1\right) + \left(3\right)$$
=
2
$$2$$
product
-1 * 3
$$\left(-1\right) * \left(3\right)$$
=
-3
$$-3$$
The graph