Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 8*x=56
- Equation x+2*y=7
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Equation x^2=-7
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Equation x^2-6*x+12=0
- Express {x} in terms of y where:
- 2*x-13*y=18
- -15*x-5*y=-8
- 16*x-10*y=-5
- -18*x-15*y=-7
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Identical expressions
- (4x- one)(six -3x)= zero
- (4x minus 1)(6 minus 3x) equally 0
- (4x minus one)(six minus 3x) equally zero
- 4x-16-3x=0
- (4x-1)(6-3x)=O
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Similar expressions
- (4x+1)(6-3x)=0
- (4x-1)(6+3x)=0
(4x-1)(6-3x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(6 - 3 x\right) \left(4 x - 1\right) = 0$$
We get the quadratic equation
$$- 12 x^{2} + 27 x - 6 = 0$$
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
$$a = -12$$
$$b = 27$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{4}$$
$$x_{2} = 2$$
$$\left(6 - 3 x\right) \left(4 x - 1\right) = 0$$
We get the quadratic equation
$$- 12 x^{2} + 27 x - 6 = 0$$
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
$$a = -12$$
$$b = 27$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(27)^2 - 4 * (-12) * (-6) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{4}$$
$$x_{2} = 2$$
Sum and product of roots
[src]
sum
2 + 1/4
$$\frac{1}{4} + 2$$
=
9/4
$$\frac{9}{4}$$
product
2 - 4
$$\frac{2}{4}$$
=
1/2
$$\frac{1}{2}$$
1/2