Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2*sin(x)=0
-
Equation 0*x=10
-
Equation (x-5)^2-x^2=3
-
Equation -2*(-y-2)-y-2=0
- Express {x} in terms of y where:
- -6*x+15*y=-13
- -17*x+14*y=11
- -11*x-3*y=-15
- 9*x-6*y=-20
-
Identical expressions
- y^ two + zero . six hundred and ninety-eight *y- twelve /(five * ten ^ thirteen)- zero . six hundred and eighty-nine * eight /(five * ten ^ twelve)= zero
- y squared plus 0.000698 multiply by y minus 12 divide by (5 multiply by 10 to the power of 13) minus 0.000689 multiply by 8 divide by (5 multiply by 10 to the power of 12) equally 0
- y to the power of two plus zero . six hundred and ninety minus eight multiply by y minus twelve divide by (five multiply by ten to the power of thirteen) minus zero . six hundred and eighty minus nine multiply by eight divide by (five multiply by ten to the power of twelve) equally zero
- y2+0.000698*y-12/(5*1013)-0.000689*8/(5*1012)=0
- y2+0.000698*y-12/5*1013-0.000689*8/5*1012=0
- y²+0.000698*y-12/(5*10^13)-0.000689*8/(5*10^12)=0
- y to the power of 2+0.000698*y-12/(5*10 to the power of 13)-0.000689*8/(5*10 to the power of 12)=0
- y^2+0.000698y-12/(510^13)-0.0006898/(510^12)=0
- y2+0.000698y-12/(51013)-0.0006898/(51012)=0
- y2+0.000698y-12/51013-0.0006898/51012=0
- y^2+0.000698y-12/510^13-0.0006898/510^12=0
- y^2+0.000698*y-12/(5*10^13)-0.000689*8/(5*10^12)=O
- y^2+0.000698*y-12 divide by (5*10^13)-0.000689*8 divide by (5*10^12)=0
-
Similar expressions
- y^2-0.000698*y-12/(5*10^13)-0.000689*8/(5*10^12)=0
- y^2+0.000698*y+12/(5*10^13)-0.000689*8/(5*10^12)=0
- y^2+0.000698*y-12/(5*10^13)+0.000689*8/(5*10^12)=0
y^2+0.000698*y-12/(5*10^13)-0.000689*8/(5*10^12)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 y + 0.000698*y - 2.4e-13 - 1.1024e-15 = 0
$$\left(\left(y^{2} + 0.000698 y\right) - 2.4 \cdot 10^{-13}\right) - 1.1024 \cdot 10^{-15} = 0$$
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
$$a = 1$$
$$b = 0.000698$$
$$c = -2.411024 \cdot 10^{-13}$$
, then
Because D > 0, then the equation has two roots.
or
$$y_{1} = 3.45418740268708 \cdot 10^{-10}$$
$$y_{2} = -0.00069800034541874$$
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
$$a = 1$$
$$b = 0.000698$$
$$c = -2.411024 \cdot 10^{-13}$$
, then
D = b^2 - 4 * a * c =
(0.000698000000000000)^2 - 4 * (1) * (-2.41102400000000e-13) = 4.87204964409600e-7
Because D > 0, then the equation has two roots.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
or
$$y_{1} = 3.45418740268708 \cdot 10^{-10}$$
$$y_{2} = -0.00069800034541874$$
Vieta's Theorem
it is reduced quadratic equation
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0.000698$$
$$q = \frac{c}{a}$$
$$q = -2.411024 \cdot 10^{-13}$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -0.000698$$
$$y_{1} y_{2} = -2.411024 \cdot 10^{-13}$$
$$p y + q + y^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0.000698$$
$$q = \frac{c}{a}$$
$$q = -2.411024 \cdot 10^{-13}$$
Vieta Formulas
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = -0.000698$$
$$y_{1} y_{2} = -2.411024 \cdot 10^{-13}$$
Rapid solution
[src]
y1 = -0.00069800034541874
$$y_{1} = -0.00069800034541874$$
y2 = 3.4541874023767e-10
$$y_{2} = 3.4541874023767 \cdot 10^{-10}$$
y2 = 3.4541874023767e-10
Sum and product of roots
[src]
sum
-0.00069800034541874 + 3.4541874023767e-10
$$-0.00069800034541874 + 3.4541874023767 \cdot 10^{-10}$$
=
-0.000698000000000000
$$-0.000698$$
product
-0.00069800034541874*3.4541874023767e-10
$$- 3.4541874023767 \cdot 10^{-10} \cdot 0.00069800034541874$$
=
-2.41102400000000e-13
$$-2.411024 \cdot 10^{-13}$$
-2.41102400000000e-13