Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation exp(x)=0
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Equation 2*x^2+5*x-25=13*x+17
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Equation x/3=15
-
Equation 3*x-15=0
- Express {x} in terms of y where:
- 9*x-19*y=-20
- 15*x+17*y=-10
- -11*x-18*y=6
- -7*x-5*y=-17
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Identical expressions
- zero .3x- fifteen ×^ two = zero
- 0.3x minus 15× squared equally 0
- zero .3x minus fifteen × to the power of two equally zero
- 0.3x-15×2=0
- 0.3x-15ײ=0
- 0.3x-15× to the power of 2=0
- 0.3x-15×^2=O
-
Similar expressions
- 0.3x+15×^2=0
0.3x-15×^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
$$a = -15$$
$$b = \frac{3}{10}$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = \frac{1}{50}$$
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
$$a = -15$$
$$b = \frac{3}{10}$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(3/10)^2 - 4 * (-15) * (0) = 9/100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = \frac{1}{50}$$
Vieta's Theorem
rewrite the equation
$$- 15 x^{2} + \frac{3 x}{10} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{50} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{50}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{50}$$
$$x_{1} x_{2} = 0$$
$$- 15 x^{2} + \frac{3 x}{10} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{x}{50} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{1}{50}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{1}{50}$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
1/50
$$\frac{1}{50}$$
=
1/50
$$\frac{1}{50}$$
product
0 -- 50
$$\frac{0}{50}$$
=
0
$$0$$
0