Mister Exam
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How to use it?
- Equation:
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Equation 3x-11=6x-4(2x-1)
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Equation 5x^2-20=0
- Equation a^2+10*a+25+(a+5)*(5-a)
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Equation 0,8(x-2)+2,6=0,5(7+x)
- Express {x} in terms of y where:
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- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 5*x+5*y=20
- Integral of d{x}:
- 5x^2-20
-
Identical expressions
- 5x^ two - twenty = zero
- 5x squared minus 20 equally 0
- 5x to the power of two minus twenty equally zero
- 5x2-20=0
- 5x²-20=0
- 5x to the power of 2-20=0
- 5x^2-20=O
-
Similar expressions
- 5x^2+20=0
5x^2-20=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
$$a = 5$$
$$b = 0$$
$$c = -20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
Simplify
$$x_{2} = -2$$
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
$$a = 5$$
$$b = 0$$
$$c = -20$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (5) * (-20) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
Simplify
$$x_{2} = -2$$
Simplify
Vieta's Theorem
rewrite the equation
$$5 x^{2} - 20 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -4$$
$$5 x^{2} - 20 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -4$$
Sum and product of roots
[src]
sum
0 - 2 + 2
$$\left(-2 + 0\right) + 2$$
=
0
$$0$$
product
1*-2*2
$$1 \left(-2\right) 2$$
=
-4
$$-4$$
-4
The graph