Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 1-5*x=-6*x+8
-
Equation 9*(x-5)=-x
-
Equation (x-2)^2=(x-9)^2
-
Equation (5x+2)(-x-4)=0
- Express {x} in terms of y where:
- 7*x+13*y=-13
- 2*x+2*y=-6
- 1*x+10*y=-18
- -7*x+7*y=-14
-
Identical expressions
- 36x^ two + one 2x+1= zero
- 36x squared plus 12x plus 1 equally 0
- 36x to the power of two plus one 2x plus 1 equally zero
- 36x2+12x+1=0
- 36x²+12x+1=0
- 36x to the power of 2+12x+1=0
- 36x^2+12x+1=O
-
Similar expressions
- 36x^2-12x+1=0
- 36x^2+12x-1=0
36x^2+12x+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 36$$
$$b = 12$$
$$c = 1$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 36 \cdot 4 \cdot 1 + 12^{2} = 0$$
Because D = 0, then the equation has one root.
$$x_{1} = - \frac{1}{6}$$
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 36$$
$$b = 12$$
$$c = 1$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 36 \cdot 4 \cdot 1 + 12^{2} = 0$$
Because D = 0, then the equation has one root.
x = -b/2a = -12/2/(36)
$$x_{1} = - \frac{1}{6}$$
Vieta's Theorem
rewrite the equation
$$36 x^{2} + 12 x + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{3} + \frac{1}{36} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{36}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{3}$$
$$x_{1} x_{2} = \frac{1}{36}$$
$$36 x^{2} + 12 x + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{3} + \frac{1}{36} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{36}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{3}$$
$$x_{1} x_{2} = \frac{1}{36}$$
Sum and product of roots
[src]
sum
-1/6
$$\left(- \frac{1}{6}\right)$$
=
-1/6
$$- \frac{1}{6}$$
product
-1/6
$$\left(- \frac{1}{6}\right)$$
=
-1/6
$$- \frac{1}{6}$$
The graph