Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=0
-
Equation z^3=1
-
Equation x^2-20=x
-
Equation 4^x+3=11^x
- Express {x} in terms of y where:
- 3*x-7*y=-5
- -17*x-2*y=7
- -20*x-12*y=13
- -8*x+2*y=11
- Graphing y =:
- x^2-20
- Factor polynomial:
- x^2-20
-
Identical expressions
- x^ two - twenty =x
- x squared minus 20 equally x
- x to the power of two minus twenty equally x
- x2-20=x
- x²-20=x
- x to the power of 2-20=x
-
Similar expressions
- x^2+20=x
x^2-20=x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 20 = x$$
to
$$- x + \left(x^{2} - 20\right) = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = -20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -4$$
left part with negative sign.
The equation is transformed from
$$x^{2} - 20 = x$$
to
$$- x + \left(x^{2} - 20\right) = 0$$
This equation is of the form
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
$$a = 1$$
$$b = -1$$
$$c = -20$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-20) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -20$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -20$$
Sum and product of roots
[src]
sum
-4 + 5
$$-4 + 5$$
=
1
$$1$$
product
-4*5
$$- 20$$
=
-20
$$-20$$
-20
The graph