Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-11)/(x-6)=11/16
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Equation cos(4*x)=0
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Equation 3/4x=12
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Equation 3x^2-5x=0
- Express {x} in terms of y where:
- 9*x+6*y=2
- -9*x+3*y=-9
- -12*x-12*y=3
- 7*x-10*y=-19
- Derivative of:
- x^2+6*x-4
-
Identical expressions
- x^ two + six *x- four = zero
- x squared plus 6 multiply by x minus 4 equally 0
- x to the power of two plus six multiply by x minus four equally zero
- x2+6*x-4=0
- x²+6*x-4=0
- x to the power of 2+6*x-4=0
- x^2+6x-4=0
- x2+6x-4=0
- x^2+6*x-4=O
-
Similar expressions
- x^2+6*x+4=0
- x^2-6*x-4=0
x^2+6*x-4=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
$$a = 1$$
$$b = 6$$
$$c = -4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3 + \sqrt{13}$$
$$x_{2} = - \sqrt{13} - 3$$
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
$$a = 1$$
$$b = 6$$
$$c = -4$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (-4) = 52
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3 + \sqrt{13}$$
$$x_{2} = - \sqrt{13} - 3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = -4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = -4$$
Rapid solution
[src]
____ x1 = -3 + \/ 13
$$x_{1} = -3 + \sqrt{13}$$
____ x2 = -3 - \/ 13
$$x_{2} = - \sqrt{13} - 3$$
x2 = -sqrt(13) - 3
Sum and product of roots
[src]
sum
____ ____ -3 + \/ 13 + -3 - \/ 13
$$\left(- \sqrt{13} - 3\right) + \left(-3 + \sqrt{13}\right)$$
=
-6
$$-6$$
product
/ ____\ / ____\ \-3 + \/ 13 /*\-3 - \/ 13 /
$$\left(-3 + \sqrt{13}\right) \left(- \sqrt{13} - 3\right)$$
=
-4
$$-4$$
-4
The graph