Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 12-x=x
-
Equation 4x+5=2x-7
-
Equation 3*x^2-9=0
-
Equation x^2-x+1=0
- Express {x} in terms of y where:
- 20*x+9*y=17
- 11*x-11*y=-17
- -17*x-12*y=-9
- -6*x+1*y=-5
- Graphing y =:
- x^2+6x+5
- Canonical form:
- x^2+6x+5
-
Identical expressions
- x^ two +6x+ five
- x squared plus 6x plus 5
- x to the power of two plus 6x plus five
- x2+6x+5
- x²+6x+5
- x to the power of 2+6x+5
-
Similar expressions
- x^2+6x-5
- x^2-6x+5
x^2+6x+5 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
$$a = 1$$
$$b = 6$$
$$c = 5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = -5$$
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
$$a = 1$$
$$b = 6$$
$$c = 5$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (5) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 5$$
Sum and product of roots
[src]
sum
-5 - 1
$$-5 - 1$$
=
-6
$$-6$$
product
-5*(-1)
$$- -5$$
=
5
$$5$$
5