Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)^2=(x-8)^2
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Equation (x+2)^5=32
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Equation x^2+3x=0
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Equation (x+2)^4-4*(x+2)^2-5=0
- Express {x} in terms of y where:
- -4*x+19*y=-13
- -5*x-6*y=-1
- -16*x-2*y=4
- -7*x+15*y=18
- 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