Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 9x-4=10x
-
Equation -x=-12
-
Equation -8x^2=0
-
Equation 7+x*(x-1)=x^2-1
- Express {x} in terms of y where:
- 3*x+2*y=20
- 13*x+17*y=-3
- -19*x+3*y=13
- -6*x-18*y=12
-
Identical expressions
- (fifteen -3x)*(x- four)= zero
- (15 minus 3x) multiply by (x minus 4) equally 0
- (fifteen minus 3x) multiply by (x minus four) equally zero
- (15-3x)(x-4)=0
- 15-3xx-4=0
- (15-3x)*(x-4)=O
-
Similar expressions
- (15+3x)*(x-4)=0
- (15-3x)*(x+4)=0
(15-3x)*(x-4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(15 - 3 x\right) \left(x - 4\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} + 27 x - 60 = 0$$
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
$$a = -3$$
$$b = 27$$
$$c = -60$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = 5$$
$$\left(15 - 3 x\right) \left(x - 4\right) = 0$$
We get the quadratic equation
$$- 3 x^{2} + 27 x - 60 = 0$$
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
$$a = -3$$
$$b = 27$$
$$c = -60$$
, then
D = b^2 - 4 * a * c =
(27)^2 - 4 * (-3) * (-60) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = 5$$
Sum and product of roots
[src]
sum
4 + 5
$$4 + 5$$
=
9
$$9$$
product
4*5
$$4 \cdot 5$$
=
20
$$20$$
20