Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x-3=10
-
Equation 2*sin(x)=0
-
Equation 4*x=-12
-
Equation x^4-x^2+1=0
- Express {x} in terms of y where:
- -12*x-6*y=-3
- -7*x-11*y=18
- -13*x+8*y=-18
- -13*x+3*y=-4
- Factor polynomial:
- x^2-8*x+7
-
Identical expressions
- x^ two - eight *x+ seven = zero
- x squared minus 8 multiply by x plus 7 equally 0
- x to the power of two minus eight multiply by x plus seven equally zero
- x2-8*x+7=0
- x²-8*x+7=0
- x to the power of 2-8*x+7=0
- x^2-8x+7=0
- x2-8x+7=0
- x^2-8*x+7=O
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Similar expressions
- x^2+8*x+7=0
- x^2-8*x-7=0
x^2-8*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
$$a = 1$$
$$b = -8$$
$$c = 7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = 1$$
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
$$a = 1$$
$$b = -8$$
$$c = 7$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (7) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = 1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 7$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 7$$
The graph