Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 25*x^3-10*x^2+x=0
-
Equation 2x^2-x-1=x^2-5x-(-1-x^2)
-
Equation 2^x=5
-
Equation (x-10)^2=(x+4)^2
- Express {x} in terms of y where:
- 15*x+12*y=-19
- -19*x-20*y=-4
- -18*x+12*y=-8
- -14*x+4*y=-16
- Integral of d{x}:
-
y^2-y
- Factor polynomial:
- y^2-y
- Graphing y =:
- y^2-y
-
Identical expressions
- y^ two -y
- y squared minus y
- y to the power of two minus y
- y2-y
- y²-y
- y to the power of 2-y
-
Similar expressions
- y^2+y
y^2-y 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:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = 1$$
$$y_{2} = 0$$
a*y^2 + b*y + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (0) = 1
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = 1$$
$$y_{2} = 0$$
Vieta's Theorem
it is reduced quadratic equation
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 1$$
$$y_{1} y_{2} = 0$$
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 1$$
$$y_{1} y_{2} = 0$$