Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation z^2+z+2=0
-
Equation 4*x^2-13*x+3=0
-
Equation 3*x^2+6*x+3=0
-
Equation 3x+5=0
- Express {x} in terms of y where:
- 2*x+11*y=15
- 2*x+14*y=-13
- 8*x+5*y=-1
- -7*x+3*y=2
- Sum of series:
-
28
- 28
-
Identical expressions
- four /7x^ two = twenty-eight
- 4 divide by 7x squared equally 28
- four divide by 7x to the power of two equally twenty minus eight
- 4/7x2=28
- 4/7x²=28
- 4/7x to the power of 2=28
- 4 divide by 7x^2=28
4/7x^2=28 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
$$\frac{4 x^{2}}{7} = 28$$
to
$$\frac{4 x^{2}}{7} - 28 = 0$$
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
$$a = \frac{4}{7}$$
$$b = 0$$
$$c = -28$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -7$$
left part with negative sign.
The equation is transformed from
$$\frac{4 x^{2}}{7} = 28$$
to
$$\frac{4 x^{2}}{7} - 28 = 0$$
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
$$a = \frac{4}{7}$$
$$b = 0$$
$$c = -28$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (4/7) * (-28) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -7$$
Vieta's Theorem
rewrite the equation
$$\frac{4 x^{2}}{7} = 28$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 49 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -49$$
$$\frac{4 x^{2}}{7} = 28$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 49 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -49$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -49$$
Sum and product of roots
[src]
sum
-7 + 7
$$-7 + 7$$
=
0
$$0$$
product
-7*7
$$- 49$$
=
-49
$$-49$$
-49