Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 6/(x-2)+5/x=3
-
Equation sin(x)=4
-
Equation 9^x-8*3^x-9=0
-
Equation x^2-6x-27=0
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -16*x-10*y=4
- Graphing y =:
- x^2-9x+8
-
Identical expressions
- x^ two -9x+ eight
- x squared minus 9x plus 8
- x to the power of two minus 9x plus eight
- x2-9x+8
- x²-9x+8
- x to the power of 2-9x+8
-
Similar expressions
- x^2+9x+8
- x^2-9x-8
x^2-9x+8 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
$$a = 1$$
$$b = -9$$
$$c = 8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = 1$$
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
$$a = 1$$
$$b = -9$$
$$c = 8$$
, then
D = b^2 - 4 * a * c =
(-9)^2 - 4 * (1) * (8) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = 1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 9$$
$$x_{1} x_{2} = 8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 9$$
$$x_{1} x_{2} = 8$$