Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 13/(x+6)=2
-
Equation x^2=18
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Equation -3(x-1)=24-10x
-
Equation 15*x^2-4*x-3=0
- Express {x} in terms of y where:
- 14*x+5*y=11
- 8*x-7*y=-1
- 20*x-5*y=-7
- 3*x-9*y=-4
- Graphing y =:
- 2*x^2+7
- Factor polynomial:
- 2*x^2+7
-
Identical expressions
- two *x^ two + seven = zero
- 2 multiply by x squared plus 7 equally 0
- two multiply by x to the power of two plus seven equally zero
- 2*x2+7=0
- 2*x²+7=0
- 2*x to the power of 2+7=0
- 2x^2+7=0
- 2x2+7=0
- 2*x^2+7=O
-
Similar expressions
- 2*x^2-7=0
2*x^2+7=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
$$a = 2$$
$$b = 0$$
$$c = 7$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{\sqrt{14} i}{2}$$
$$x_{2} = - \frac{\sqrt{14} i}{2}$$
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
$$a = 2$$
$$b = 0$$
$$c = 7$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (2) * (7) = -56
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{14} i}{2}$$
$$x_{2} = - \frac{\sqrt{14} i}{2}$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} + 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{7}{2}$$
$$2 x^{2} + 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{7}{2}$$
Sum and product of roots
[src]
sum
____ ____
I*\/ 14 I*\/ 14
- -------- + --------
2 2
$$- \frac{\sqrt{14} i}{2} + \frac{\sqrt{14} i}{2}$$
=
0
$$0$$
product
____ ____
-I*\/ 14 I*\/ 14
----------*--------
2 2
$$- \frac{\sqrt{14} i}{2} \frac{\sqrt{14} i}{2}$$
=
7/2
$$\frac{7}{2}$$
7/2
Rapid solution
[src]
____
-I*\/ 14
x1 = ----------
2
$$x_{1} = - \frac{\sqrt{14} i}{2}$$
____
I*\/ 14
x2 = --------
2
$$x_{2} = \frac{\sqrt{14} i}{2}$$
x2 = sqrt(14)*i/2
The graph