Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 8x-15=-12+5x
-
Equation x^2-x-7=0
-
Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
-
Equation x^3-6*x^2+x-6=0
- Express {x} in terms of y where:
- -19*x+1*y=-6
- 16*x-9*y=-17
- 2*x+4*y=-1
- -14*x-5*y=-3
- Graphing y =:
- x^2-2*x-10
-
Identical expressions
- x^ two - two *x- ten = zero
- x squared minus 2 multiply by x minus 10 equally 0
- x to the power of two minus two multiply by x minus ten equally zero
- x2-2*x-10=0
- x²-2*x-10=0
- x to the power of 2-2*x-10=0
- x^2-2x-10=0
- x2-2x-10=0
- x^2-2*x-10=O
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Similar expressions
- x^2-2*x+10=0
- x^2+2*x-10=0
x^2-2*x-10=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
$$a = 1$$
$$b = -2$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1 + \sqrt{11}$$
$$x_{2} = 1 - \sqrt{11}$$
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
$$a = 1$$
$$b = -2$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-10) = 44
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1 + \sqrt{11}$$
$$x_{2} = 1 - \sqrt{11}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -10$$
Sum and product of roots
[src]
sum
____ ____ 1 - \/ 11 + 1 + \/ 11
$$\left(1 - \sqrt{11}\right) + \left(1 + \sqrt{11}\right)$$
=
2
$$2$$
product
/ ____\ / ____\ \1 - \/ 11 /*\1 + \/ 11 /
$$\left(1 - \sqrt{11}\right) \left(1 + \sqrt{11}\right)$$
=
-10
$$-10$$
-10
Rapid solution
[src]
____ x1 = 1 - \/ 11
$$x_{1} = 1 - \sqrt{11}$$
____ x2 = 1 + \/ 11
$$x_{2} = 1 + \sqrt{11}$$
x2 = 1 + sqrt(11)
The graph