Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx=-1/2
- Equation 3a^2-21=0
- Equation 13*x^2-330*x-208=0
-
Equation sqrt(3)*sin(x)=1-cos(x)
- Express {x} in terms of y where:
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- 10*x-1*y=10
- 15*x-17*y=19
-
Identical expressions
- thirteen *x^ two - three hundred and thirty *x- two hundred and eight = zero
- 13 multiply by x squared minus 330 multiply by x minus 208 equally 0
- thirteen multiply by x to the power of two minus three hundred and thirty multiply by x minus two hundred and eight equally zero
- 13*x2-330*x-208=0
- 13*x²-330*x-208=0
- 13*x to the power of 2-330*x-208=0
- 13x^2-330x-208=0
- 13x2-330x-208=0
- 13*x^2-330*x-208=O
-
Similar expressions
- 13*x^2+330*x-208=0
- 13*x^2-330*x+208=0
13*x^2-330*x-208=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
$$a = 13$$
$$b = -330$$
$$c = -208$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 26$$
$$x_{2} = - \frac{8}{13}$$
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
$$a = 13$$
$$b = -330$$
$$c = -208$$
, then
D = b^2 - 4 * a * c =
(-330)^2 - 4 * (13) * (-208) = 119716
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 26$$
$$x_{2} = - \frac{8}{13}$$
Vieta's Theorem
rewrite the equation
$$\left(13 x^{2} - 330 x\right) - 208 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{330 x}{13} - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{330}{13}$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{330}{13}$$
$$x_{1} x_{2} = -16$$
$$\left(13 x^{2} - 330 x\right) - 208 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{330 x}{13} - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{330}{13}$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{330}{13}$$
$$x_{1} x_{2} = -16$$
Sum and product of roots
[src]
sum
26 - 8/13
$$- \frac{8}{13} + 26$$
=
330 --- 13
$$\frac{330}{13}$$
product
26*(-8) ------- 13
$$\frac{\left(-8\right) 26}{13}$$
=
-16
$$-16$$
-16