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How to use it?
- Equation:
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Equation x^2-2x-15=0
- Equation x^4-29x^2+100=0
-
Equation 85+(68÷x)×15=145
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Equation sin6x+√3cos6x=-2cos8x.
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- 10*x-1*y=10
- Graphing y =:
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x^2-2x-15
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Identical expressions
- x^ two -2x- fifteen = zero
- x squared minus 2x minus 15 equally 0
- x to the power of two minus 2x minus fifteen equally zero
- x2-2x-15=0
- x²-2x-15=0
- x to the power of 2-2x-15=0
- x^2-2x-15=O
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Similar expressions
- x^2-2x+15=0
- x^2+2x-15=0
x^2-2x-15=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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
Simplify
$$x_{2} = -3$$
Simplify
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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-15) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
Simplify
$$x_{2} = -3$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -15$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -15$$
Sum and product of roots
[src]
sum
0 - 3 + 5
$$\left(-3 + 0\right) + 5$$
=
2
$$2$$
product
1*-3*5
$$1 \left(-3\right) 5$$
=
-15
$$-15$$
-15
The graph