Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -20*(x-13)=-220
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Equation x-x/12=55/12
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Equation 3^x=81
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Equation 12-x^2=11
- Express {x} in terms of y where:
- 18*x+19*y=7
- 1*x+6*y=6
- 20*x+9*y=17
- 11*x-11*y=-17
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Identical expressions
- 1 zero x-8x^ two * three =0
- 10x minus 8x squared multiply by 3 equally 0
- 1 zero x minus 8x to the power of two multiply by three equally 0
- 10x-8x2*3=0
- 10x-8x²*3=0
- 10x-8x to the power of 2*3=0
- 10x-8x^23=0
- 10x-8x23=0
- 10x-8x^2*3=O
-
Similar expressions
- 10x+8x^2*3=0
10x-8x^2*3=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
$$a = -24$$
$$b = 10$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = \frac{5}{12}$$
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
$$a = -24$$
$$b = 10$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (-24) * (0) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = \frac{5}{12}$$
Vieta's Theorem
rewrite the equation
$$10 x - 3 \cdot 8 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{12} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{12}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{12}$$
$$x_{1} x_{2} = 0$$
$$10 x - 3 \cdot 8 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{12} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{12}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{12}$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
5/12
$$\frac{5}{12}$$
=
5/12
$$\frac{5}{12}$$
product
0*5 --- 12
$$\frac{0 \cdot 5}{12}$$
=
0
$$0$$
0