Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)-x=0
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Equation 15-4(7-x)=11
-
Equation x+(8-3x)=12
-
Equation 3*x-4/6=7/8
- Express {x} in terms of y where:
- 2*x+11*y=0
- 14*x-17*y=-4
- 18*x-10*y=-9
- -16*x-14*y=-18
- Graphing y =:
- x^2+8*x-16
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Identical expressions
- x^ two + eight *x- sixteen = zero
- x squared plus 8 multiply by x minus 16 equally 0
- x to the power of two plus eight multiply by x minus sixteen equally zero
- x2+8*x-16=0
- x²+8*x-16=0
- x to the power of 2+8*x-16=0
- x^2+8x-16=0
- x2+8x-16=0
- x^2+8*x-16=O
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Similar expressions
- x^2-8*x-16=0
- x^2+8*x+16=0
x^2+8*x-16=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
$$a = 1$$
$$b = 8$$
$$c = -16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4 + 4 \sqrt{2}$$
$$x_{2} = - 4 \sqrt{2} - 4$$
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
$$a = 1$$
$$b = 8$$
$$c = -16$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (1) * (-16) = 128
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4 + 4 \sqrt{2}$$
$$x_{2} = - 4 \sqrt{2} - 4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = -16$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = -16$$
Rapid solution
[src]
___ x1 = -4 + 4*\/ 2
$$x_{1} = -4 + 4 \sqrt{2}$$
___ x2 = -4 - 4*\/ 2
$$x_{2} = - 4 \sqrt{2} - 4$$
x2 = -4*sqrt(2) - 4
Sum and product of roots
[src]
sum
___ ___ -4 + 4*\/ 2 + -4 - 4*\/ 2
$$\left(- 4 \sqrt{2} - 4\right) + \left(-4 + 4 \sqrt{2}\right)$$
=
-8
$$-8$$
product
/ ___\ / ___\ \-4 + 4*\/ 2 /*\-4 - 4*\/ 2 /
$$\left(-4 + 4 \sqrt{2}\right) \left(- 4 \sqrt{2} - 4\right)$$
=
-16
$$-16$$
-16
The graph