Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+2x+1=0
-
Equation -x=0
-
Equation 5*x=50
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Equation x^2=17
- Express {x} in terms of y where:
- -10*x-12*y=-15
- -8*x-18*y=15
- -20*x-4*y=-12
- -16*x+1*y=3
- Graphing y =:
- x^2
- Derivative of:
-
x^2
-
17
- Integral of d{x}:
-
x^2
- Sum of series:
-
17
- Limit of the function:
-
17
-
Identical expressions
- x^ two = seventeen
- x squared equally 17
- x to the power of two equally seventeen
- x2=17
- x²=17
- x to the power of 2=17
-
Similar expressions
- x^2-9*x+14=0
x^2=17 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} = 17$$
to
$$x^{2} - 17 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -17$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{17}$$
$$x_{2} = - \sqrt{17}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 17$$
to
$$x^{2} - 17 = 0$$
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 - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = -17$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-17) = 68
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{17}$$
$$x_{2} = - \sqrt{17}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -17$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -17$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -17$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -17$$
Rapid solution
[src]
____ x1 = -\/ 17
$$x_{1} = - \sqrt{17}$$
____ x2 = \/ 17
$$x_{2} = \sqrt{17}$$
x2 = sqrt(17)
Sum and product of roots
[src]
sum
____ ____ - \/ 17 + \/ 17
$$- \sqrt{17} + \sqrt{17}$$
=
0
$$0$$
product
____ ____ -\/ 17 *\/ 17
$$- \sqrt{17} \sqrt{17}$$
=
-17
$$-17$$
-17
The graph