Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 10/(x+6)=1
-
Equation x^6=-64
-
Equation sin(5*x)=-1
-
Equation 5(x-7)=-3
- Express {x} in terms of y where:
- -5*x-13*y=-2
- -6*x-14*y=17
- -11*x-3*y=-1
- 16*x+7*y=-9
- Derivative of:
-
16x^2
- The double integral of:
- 16x^2
- Canonical form:
- 16x^2
-
Identical expressions
- one 6x^ two =1
- 16x squared equally 1
- one 6x to the power of two equally 1
- 16x2=1
- 16x²=1
- 16x to the power of 2=1
16x^2=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$16 x^{2} = 1$$
to
$$16 x^{2} - 1 = 0$$
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
$$a = 16$$
$$b = 0$$
$$c = -1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{4}$$
$$x_{2} = - \frac{1}{4}$$
left part with negative sign.
The equation is transformed from
$$16 x^{2} = 1$$
to
$$16 x^{2} - 1 = 0$$
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 - it is the discriminant.
Because
$$a = 16$$
$$b = 0$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (16) * (-1) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{4}$$
$$x_{2} = - \frac{1}{4}$$
Vieta's Theorem
rewrite the equation
$$16 x^{2} = 1$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{1}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{1}{16}$$
$$16 x^{2} = 1$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{1}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{1}{16}$$
Sum and product of roots
[src]
sum
-1/4 + 1/4
$$- \frac{1}{4} + \frac{1}{4}$$
=
0
$$0$$
product
-1 --- 4*4
$$- \frac{1}{16}$$
=
-1/16
$$- \frac{1}{16}$$
-1/16
The graph