Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation (x-11)*(-x+9)=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
- Graphing y =:
- 2x^2+3x+1
- Derivative of:
- 2x^2+3x+1
- Canonical form:
- 2x^2+3x+1
-
Identical expressions
- two x^2+3x+ one = zero
- 2x squared plus 3x plus 1 equally 0
- two x squared plus 3x plus one equally zero
- 2x2+3x+1=0
- 2x²+3x+1=0
- 2x to the power of 2+3x+1=0
- 2x^2+3x+1=O
-
Similar expressions
- 2x^2-3x+1=0
- 2x^2+3x-1=0
2x^2+3x+1=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
$$a = 2$$
$$b = 3$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = -1$$
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
$$a = 2$$
$$b = 3$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (2) * (1) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} + 3 x\right) + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{3 x}{2} + \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{3}{2}$$
$$x_{1} x_{2} = \frac{1}{2}$$
$$\left(2 x^{2} + 3 x\right) + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{3 x}{2} + \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{3}{2}$$
$$x_{1} x_{2} = \frac{1}{2}$$
Sum and product of roots
[src]
sum
-1 - 1/2
$$-1 - \frac{1}{2}$$
=
-3/2
$$- \frac{3}{2}$$
product
-(-1) ------ 2
$$- \frac{-1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2
The graph