Mister Exam
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How to use it?
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Equation 3*x^2-9=0
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Equation x^2-x+1=0
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Identical expressions
- two x^ two -5x+2= zero
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Similar expressions
- 2x^2+5x+2=0
- 2x^2-5x-2=0
2x^2-5x+2=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
$$a = 2$$
$$b = -5$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = \frac{1}{2}$$
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
$$a = 2$$
$$b = -5$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (2) * (2) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = \frac{1}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} - 5 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = 1$$
$$\left(2 x^{2} - 5 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{2}$$
$$x_{1} x_{2} = 1$$
Sum and product of roots
[src]
sum
1/2 + 2
$$\frac{1}{2} + 2$$
=
5/2
$$\frac{5}{2}$$
product
2 - 2
$$\frac{2}{2}$$
=
1
$$1$$
1
The graph