Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation e^x=0
-
Equation 10*(x-9)=7
-
Equation cos(x)=3
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Equation 3-3*6+2=x
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-15*y=-4
- 1*x+5*y=-11
- -11*x-15*y=14
- Graphing y =:
- x^2+x-6
- Factor squared:
- x^2+x-6
- Integral of d{x}:
-
x^2+x-6
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Identical expressions
- x^ two +x- six
- x squared plus x minus 6
- x to the power of two plus x minus six
- x2+x-6
- x²+x-6
- x to the power of 2+x-6
-
Similar expressions
- x^2+x+6
- x^2-x-6
x^2+x-6 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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -3$$
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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-6) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -6$$
Sum and product of roots
[src]
sum
-3 + 2
$$-3 + 2$$
=
-1
$$-1$$
product
-3*2
$$- 6$$
=
-6
$$-6$$
-6