Mister Exam
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How to use it?
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Equation x:12=17
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Identical expressions
- two *x^ two - seven = zero
- 2 multiply by x squared minus 7 equally 0
- two multiply by x to the power of two minus seven equally zero
- 2*x2-7=0
- 2*x²-7=0
- 2*x to the power of 2-7=0
- 2x^2-7=0
- 2x2-7=0
- 2*x^2-7=O
-
Similar expressions
- 2*x^2+7=0
2*x^2-7=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
$$a = 2$$
$$b = 0$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{14}}{2}$$
$$x_{2} = - \frac{\sqrt{14}}{2}$$
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
$$a = 2$$
$$b = 0$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (2) * (-7) = 56
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{14}}{2}$$
$$x_{2} = - \frac{\sqrt{14}}{2}$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{7}{2}$$
$$2 x^{2} - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{7}{2}$$
Rapid solution
[src]
____
-\/ 14
x1 = --------
2
$$x_{1} = - \frac{\sqrt{14}}{2}$$
____
\/ 14
x2 = ------
2
$$x_{2} = \frac{\sqrt{14}}{2}$$
x2 = sqrt(14)/2
Sum and product of roots
[src]
sum
____ ____
\/ 14 \/ 14
- ------ + ------
2 2
$$- \frac{\sqrt{14}}{2} + \frac{\sqrt{14}}{2}$$
=
0
$$0$$
product
____ ____ -\/ 14 \/ 14 --------*------ 2 2
$$- \frac{\sqrt{14}}{2} \frac{\sqrt{14}}{2}$$
=
-7/2
$$- \frac{7}{2}$$
-7/2