Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tan(x)=-1/2
-
Equation 1*(x-1)*(x-3)=0
-
Equation 5x+12=8x+30
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- -2*x-19*y=3
- -2*x+18*y=13
- -2*x-15*y=-1
- 10*x-2*y=11
-
Identical expressions
- x^ two - eleven *x+ thirty = zero
- x squared minus 11 multiply by x plus 30 equally 0
- x to the power of two minus eleven multiply by x plus thirty equally zero
- x2-11*x+30=0
- x²-11*x+30=0
- x to the power of 2-11*x+30=0
- x^2-11x+30=0
- x2-11x+30=0
- x^2-11*x+30=O
-
Similar expressions
- x^2-11*x-30=0
- x^2+11*x+30=0
x^2-11*x+30=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
$$a = 1$$
$$b = -11$$
$$c = 30$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = 5$$
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
$$a = 1$$
$$b = -11$$
$$c = 30$$
, then
D = b^2 - 4 * a * c =
(-11)^2 - 4 * (1) * (30) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = 5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = 30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 11$$
$$x_{1} x_{2} = 30$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = 30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 11$$
$$x_{1} x_{2} = 30$$
Sum and product of roots
[src]
sum
5 + 6
$$5 + 6$$
=
11
$$11$$
product
5*6
$$5 \cdot 6$$
=
30
$$30$$
30
The graph