Mister Exam
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How to use it?
- Equation:
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Equation (y^4+4*y^2-12)/4=0
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Equation -x=5
- Express {x} in terms of y where:
- -14*x-8*y=20
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- Graphing y =:
- -x^2+6*x+16
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Identical expressions
- -x^ two + six *x+ sixteen = zero
- minus x squared plus 6 multiply by x plus 16 equally 0
- minus x to the power of two plus six multiply by x plus sixteen equally zero
- -x2+6*x+16=0
- -x²+6*x+16=0
- -x to the power of 2+6*x+16=0
- -x^2+6x+16=0
- -x2+6x+16=0
- -x^2+6*x+16=O
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Similar expressions
- -x^2-6*x+16=0
- -x^2+6*x-16=0
- x^2+6*x+16=0
-x^2+6*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
$$a = -1$$
$$b = 6$$
$$c = 16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = 8$$
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
$$a = -1$$
$$b = 6$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (-1) * (16) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = 8$$
Vieta's Theorem
rewrite the equation
$$\left(- x^{2} + 6 x\right) + 16 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -16$$
$$\left(- x^{2} + 6 x\right) + 16 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 x - 16 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -6$$
$$q = \frac{c}{a}$$
$$q = -16$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 6$$
$$x_{1} x_{2} = -16$$
Sum and product of roots
[src]
sum
-2 + 8
$$-2 + 8$$
=
6
$$6$$
product
-2*8
$$- 16$$
=
-16
$$-16$$
-16
The graph