Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 7*x=0
-
Equation 3x-2=x+4
-
Equation tan(x)=7
-
Equation (x-3)(x^2-2x+1)=3(x-1)
- Express {x} in terms of y where:
- 18*x-10*y=-9
- 18*x-12*y=-9
- 12*x+11*y=20
- 19*x-12*y=-9
- Factor squared:
- x^2-12*x+7
-
Identical expressions
- x^ two - twelve *x+ seven = zero
- x squared minus 12 multiply by x plus 7 equally 0
- x to the power of two minus twelve multiply by x plus seven equally zero
- x2-12*x+7=0
- x²-12*x+7=0
- x to the power of 2-12*x+7=0
- x^2-12x+7=0
- x2-12x+7=0
- x^2-12*x+7=O
-
Similar expressions
- x^2-12*x-7=0
- x^2+12*x+7=0
x^2-12*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
$$a = 1$$
$$b = -12$$
$$c = 7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{29} + 6$$
$$x_{2} = 6 - \sqrt{29}$$
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
$$a = 1$$
$$b = -12$$
$$c = 7$$
, then
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (1) * (7) = 116
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{29} + 6$$
$$x_{2} = 6 - \sqrt{29}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = 7$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = 7$$
Rapid solution
[src]
____ x1 = 6 - \/ 29
$$x_{1} = 6 - \sqrt{29}$$
____ x2 = 6 + \/ 29
$$x_{2} = \sqrt{29} + 6$$
x2 = sqrt(29) + 6
Sum and product of roots
[src]
sum
____ ____ 6 - \/ 29 + 6 + \/ 29
$$\left(6 - \sqrt{29}\right) + \left(\sqrt{29} + 6\right)$$
=
12
$$12$$
product
/ ____\ / ____\ \6 - \/ 29 /*\6 + \/ 29 /
$$\left(6 - \sqrt{29}\right) \left(\sqrt{29} + 6\right)$$
=
7
$$7$$
7
The graph