Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3=x^2+2x
- Equation x^3+6x^2-x-6=0
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Equation (x-1)*(x^2+8*x+16)=6*(x+4)
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Equation 4*x-8=x+1
- Express {x} in terms of y where:
- -6*x-17*y=-3
- -13*x-15*y=-9
- -4*x+16*y=-14
- 6*x+7*y=-1
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Identical expressions
- (six -4x)(x+ nine)= zero
- (6 minus 4x)(x plus 9) equally 0
- (six minus 4x)(x plus nine) equally zero
- 6-4xx+9=0
- (6-4x)(x+9)=O
-
Similar expressions
- (6-4x)(x-9)=0
- (6+4x)(x+9)=0
(6-4x)(x+9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(6 - 4 x\right) \left(x + 9\right) = 0$$
We get the quadratic equation
$$- 4 x^{2} - 30 x + 54 = 0$$
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
$$a = -4$$
$$b = -30$$
$$c = 54$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -9$$
$$x_{2} = \frac{3}{2}$$
$$\left(6 - 4 x\right) \left(x + 9\right) = 0$$
We get the quadratic equation
$$- 4 x^{2} - 30 x + 54 = 0$$
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
$$a = -4$$
$$b = -30$$
$$c = 54$$
, then
D = b^2 - 4 * a * c =
(-30)^2 - 4 * (-4) * (54) = 1764
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -9$$
$$x_{2} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
-9 + 3/2
$$-9 + \frac{3}{2}$$
=
-15/2
$$- \frac{15}{2}$$
product
-9*3 ---- 2
$$- \frac{27}{2}$$
=
-27/2
$$- \frac{27}{2}$$
-27/2