Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=4
-
Equation 5^x=125
-
Equation (|x+4|)=5
-
Equation 2*sin(x)=1
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -5*x-2*y=9
- Canonical form:
- x^2-11
- Integral of d{x}:
- x^2-11
- Graphing y =:
- x^2-11
-
Identical expressions
- x^ two - eleven = zero
- x squared minus 11 equally 0
- x to the power of two minus eleven equally zero
- x2-11=0
- x²-11=0
- x to the power of 2-11=0
- x^2-11=O
-
Similar expressions
- x^2+11=0
x^2-11=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
$$a = 1$$
$$b = 0$$
$$c = -11$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{11}$$
$$x_{2} = - \sqrt{11}$$
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
$$a = 1$$
$$b = 0$$
$$c = -11$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-11) = 44
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{11}$$
$$x_{2} = - \sqrt{11}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -11$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -11$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -11$$
Sum and product of roots
[src]
sum
____ ____ - \/ 11 + \/ 11
$$- \sqrt{11} + \sqrt{11}$$
=
0
$$0$$
product
____ ____ -\/ 11 *\/ 11
$$- \sqrt{11} \sqrt{11}$$
=
-11
$$-11$$
-11
Rapid solution
[src]
____ x1 = -\/ 11
$$x_{1} = - \sqrt{11}$$
____ x2 = \/ 11
$$x_{2} = \sqrt{11}$$
x2 = sqrt(11)
The graph