Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=2/3
- Equation x+y=3
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Equation (x-11)^4=(x+3)^4
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Equation 9-4x=3x-40
- Express {x} in terms of y where:
- 6*x+17*y=3
- -17*x+18*y=10
- 10*x-18*y=3
- 13*x-12*y=19
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Identical expressions
- (6x- twenty-four)*(x+ nineteen)= zero
- (6x minus 24) multiply by (x plus 19) equally 0
- (6x minus twenty minus four) multiply by (x plus nineteen) equally zero
- (6x-24)(x+19)=0
- 6x-24x+19=0
- (6x-24)*(x+19)=O
-
Similar expressions
- (6x-24)*(x-19)=0
- (6x+24)*(x+19)=0
(6x-24)*(x+19)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 19\right) \left(6 x - 24\right) = 0$$
We get the quadratic equation
$$6 x^{2} + 90 x - 456 = 0$$
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
$$a = 6$$
$$b = 90$$
$$c = -456$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -19$$
$$\left(x + 19\right) \left(6 x - 24\right) = 0$$
We get the quadratic equation
$$6 x^{2} + 90 x - 456 = 0$$
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
$$a = 6$$
$$b = 90$$
$$c = -456$$
, then
D = b^2 - 4 * a * c =
(90)^2 - 4 * (6) * (-456) = 19044
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -19$$
Sum and product of roots
[src]
sum
-19 + 4
$$-19 + 4$$
=
-15
$$-15$$
product
-19*4
$$- 76$$
=
-76
$$-76$$
-76