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