Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x+10)^2=(5-x)^2
-
Equation k^2-2*k+2=0
-
Equation x^2+x-20=0
-
Equation x^5-x^4-2x^3+2x^2-3x+3=0
- Express {x} in terms of y where:
- -10*x+18*y=6
- 9*x-18*y=6
- -1*x+19*y=-10
- 4*x+13*y=13
- Factor polynomial:
- x^2+x-20
- Factor squared:
- x^2+x-20
-
Identical expressions
- x^ two +x- twenty = zero
- x squared plus x minus 20 equally 0
- x to the power of two plus x minus twenty equally zero
- x2+x-20=0
- x²+x-20=0
- x to the power of 2+x-20=0
- x^2+x-20=O
-
Similar expressions
- x^2-x-20=0
- x^2+x+20=0
x^2+x-20=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
$$a = 1$$
$$b = 1$$
$$c = -20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -5$$
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
$$x_{1} = 4$$
$$x_{2} = -5$$
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
-5 + 4
$$-5 + 4$$
=
-1
$$-1$$
product
-5*4
$$- 20$$
=
-20
$$-20$$
-20
The graph