Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation a*x=b
-
Equation 2-3(2+3x)=14
-
Equation x^2-x+8=0
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Equation 2^x=7
- Express {x} in terms of y where:
- 8*x-4*y=10
- -17*x-5*y=-20
- 2*x+19*y=-7
- -4*x+7*y=-16
- Graphing y =:
- x^2+10x
- Canonical form:
- x^2+10x
-
Identical expressions
- x^ two +1 zero x=0
- x squared plus 10x equally 0
- x to the power of two plus 1 zero x equally 0
- x2+10x=0
- x²+10x=0
- x to the power of 2+10x=0
- x^2+10x=O
-
Similar expressions
- x^2-10x=0
x^2+10x=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
$$a = 1$$
$$b = 10$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = -10$$
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
$$a = 1$$
$$b = 10$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (0) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = -10$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 10$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -10$$
$$x_{1} x_{2} = 0$$
The graph