Mister Exam
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How to use it?
- Equation:
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Equation x^3=3
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Equation sin(x)=√3/2
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Equation x^2+9x=0
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Equation sin(x)=-3/2
- Express {x} in terms of y where:
- 20*x-5*y=-7
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Identical expressions
- five *x^ two - twelve *x+ four = zero
- 5 multiply by x squared minus 12 multiply by x plus 4 equally 0
- five multiply by x to the power of two minus twelve multiply by x plus four equally zero
- 5*x2-12*x+4=0
- 5*x²-12*x+4=0
- 5*x to the power of 2-12*x+4=0
- 5x^2-12x+4=0
- 5x2-12x+4=0
- 5*x^2-12*x+4=O
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Similar expressions
- 5*x^2-12*x-4=0
- 5*x^2+12*x+4=0
5*x^2-12*x+4=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
$$a = 5$$
$$b = -12$$
$$c = 4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = \frac{2}{5}$$
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
$$a = 5$$
$$b = -12$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (5) * (4) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = \frac{2}{5}$$
Vieta's Theorem
rewrite the equation
$$\left(5 x^{2} - 12 x\right) + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{12 x}{5} + \frac{4}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{12}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{12}{5}$$
$$x_{1} x_{2} = \frac{4}{5}$$
$$\left(5 x^{2} - 12 x\right) + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{12 x}{5} + \frac{4}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{12}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{12}{5}$$
$$x_{1} x_{2} = \frac{4}{5}$$
Sum and product of roots
[src]
sum
2 + 2/5
$$\frac{2}{5} + 2$$
=
12/5
$$\frac{12}{5}$$
product
2*2 --- 5
$$\frac{2 \cdot 2}{5}$$
=
4/5
$$\frac{4}{5}$$
4/5
The graph