Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 49*x^3+14*x^2+x=0
-
Equation 4^x=8
-
Equation x^2-x=12
-
Equation x-5(x+3)=5
- Express {x} in terms of y where:
- -7*x-13*y=-12
- -3*x+19*y=16
- -4*x+4*y=-9
- -19*x-2*y=-6
- Graphing y =:
- x^2+6*x+7
- Factor polynomial:
- x^2+6*x+7
- Factor squared:
- x^2+6*x+7
-
Identical expressions
- x^ two + six *x+ seven = zero
- x squared plus 6 multiply by x plus 7 equally 0
- x to the power of two plus six multiply by x plus seven equally zero
- x2+6*x+7=0
- x²+6*x+7=0
- x to the power of 2+6*x+7=0
- x^2+6x+7=0
- x2+6x+7=0
- x^2+6*x+7=O
-
Similar expressions
- x^2+6*x-7=0
- x^2-6*x+7=0
x^2+6*x+7=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
$$a = 1$$
$$b = 6$$
$$c = 7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3 + \sqrt{2}$$
$$x_{2} = -3 - \sqrt{2}$$
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
$$a = 1$$
$$b = 6$$
$$c = 7$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (7) = 8
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3 + \sqrt{2}$$
$$x_{2} = -3 - \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 7$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 7$$
Rapid solution
[src]
___ x1 = -3 - \/ 2
$$x_{1} = -3 - \sqrt{2}$$
___ x2 = -3 + \/ 2
$$x_{2} = -3 + \sqrt{2}$$
x2 = -3 + sqrt(2)
Sum and product of roots
[src]
sum
___ ___ -3 - \/ 2 + -3 + \/ 2
$$\left(-3 - \sqrt{2}\right) + \left(-3 + \sqrt{2}\right)$$
=
-6
$$-6$$
product
/ ___\ / ___\ \-3 - \/ 2 /*\-3 + \/ 2 /
$$\left(-3 - \sqrt{2}\right) \left(-3 + \sqrt{2}\right)$$
=
7
$$7$$
7
The graph