Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)^4-4*(x+2)^2-5=0
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Graphing y =:
- 2x^2-5x-12
-
Identical expressions
- two x^2-5x- twelve = zero
- 2x squared minus 5x minus 12 equally 0
- two x squared minus 5x minus twelve equally zero
- 2x2-5x-12=0
- 2x²-5x-12=0
- 2x to the power of 2-5x-12=0
- 2x^2-5x-12=O
-
Similar expressions
- 2x^2+5x-12=0
- 2x^2-5x+12=0
2x^2-5x-12=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
$$a = 2$$
$$b = -5$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = - \frac{3}{2}$$
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
$$a = 2$$
$$b = -5$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (2) * (-12) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = - \frac{3}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} - 5 x\right) - 12 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = -6$$
$$\left(2 x^{2} - 5 x\right) - 12 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = -6$$
Sum and product of roots
[src]
sum
4 - 3/2
$$- \frac{3}{2} + 4$$
=
5/2
$$\frac{5}{2}$$
product
4*(-3) ------ 2
$$\frac{\left(-3\right) 4}{2}$$
=
-6
$$-6$$
-6