Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*x^2+6*x+9=0
-
Equation 10(x-9)=7
-
Equation (x+2)^4+(x+2)^2-12=0
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Equation (x+9)^2=(x+6)^2
- Express {x} in terms of y where:
- -6*x-17*y=14
- 4*x-18*y=-14
- -14*x-1*y=3
- 1*x-6*y=-19
- Graphing y =:
- 2*x^2+6*x+9
- Factor polynomial:
- 2*x^2+6*x+9
- Plot:
- 2*x^2+6*x+9
-
Identical expressions
- two *x^ two + six *x+ nine = zero
- 2 multiply by x squared plus 6 multiply by x plus 9 equally 0
- two multiply by x to the power of two plus six multiply by x plus nine equally zero
- 2*x2+6*x+9=0
- 2*x²+6*x+9=0
- 2*x to the power of 2+6*x+9=0
- 2x^2+6x+9=0
- 2x2+6x+9=0
- 2*x^2+6*x+9=O
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Similar expressions
- 2*x^2-6*x+9=0
- 2*x^2+6*x-9=0
2*x^2+6*x+9=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
$$a = 2$$
$$b = 6$$
$$c = 9$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{3}{2} + \frac{3 i}{2}$$
$$x_{2} = - \frac{3}{2} - \frac{3 i}{2}$$
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
$$a = 2$$
$$b = 6$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (2) * (9) = -36
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
$$x_{1} = - \frac{3}{2} + \frac{3 i}{2}$$
$$x_{2} = - \frac{3}{2} - \frac{3 i}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} + 6 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 3 x + \frac{9}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = \frac{9}{2}$$
$$\left(2 x^{2} + 6 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 3 x + \frac{9}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = \frac{9}{2}$$
Rapid solution
[src]
3 3*I
x1 = - - - ---
2 2
$$x_{1} = - \frac{3}{2} - \frac{3 i}{2}$$
3 3*I
x2 = - - + ---
2 2
$$x_{2} = - \frac{3}{2} + \frac{3 i}{2}$$
x2 = -3/2 + 3*i/2
Sum and product of roots
[src]
sum
3 3*I 3 3*I - - - --- + - - + --- 2 2 2 2
$$\left(- \frac{3}{2} - \frac{3 i}{2}\right) + \left(- \frac{3}{2} + \frac{3 i}{2}\right)$$
=
-3
$$-3$$
product
/ 3 3*I\ / 3 3*I\ |- - - ---|*|- - + ---| \ 2 2 / \ 2 2 /
$$\left(- \frac{3}{2} - \frac{3 i}{2}\right) \left(- \frac{3}{2} + \frac{3 i}{2}\right)$$
=
9/2
$$\frac{9}{2}$$
9/2
The graph