Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation |x^2-1|-|x-3|=7
-
Equation cos(x)+sin(x)=0
-
Equation 5-2*x=11-7*(x+2)
-
Equation 3*x+50=77
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 1*x-6*y=-19
- -6*x-17*y=14
- 18*x-12*y=-20
-
Identical expressions
- x^ two +2x- twenty-four = zero
- x squared plus 2x minus 24 equally 0
- x to the power of two plus 2x minus twenty minus four equally zero
- x2+2x-24=0
- x²+2x-24=0
- x to the power of 2+2x-24=0
- x^2+2x-24=O
-
Similar expressions
- x^2-2x-24=0
- x^2+2x+24=0
x^2+2x-24=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = 2$$
$$c = -24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -6$$
Simplify
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
$$a = 1$$
$$b = 2$$
$$c = -24$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (-24) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
Simplify
$$x_{2} = -6$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -24$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -24$$
Sum and product of roots
[src]
sum
0 - 6 + 4
$$\left(-6 + 0\right) + 4$$
=
-2
$$-2$$
product
1*-6*4
$$1 \left(-6\right) 4$$
=
-24
$$-24$$
-24
The graph