Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9^x-8*3^x-9=0
- Equation x+y=4
-
Equation 5x+8=-12
-
Equation x/9+x=-3
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
-
Identical expressions
- one +3x-1 zero x^ two =0
- 1 plus 3x minus 10x squared equally 0
- one plus 3x minus 1 zero x to the power of two equally 0
- 1+3x-10x2=0
- 1+3x-10x²=0
- 1+3x-10x to the power of 2=0
- 1+3x-10x^2=O
-
Similar expressions
- 1-3x-10x^2=0
- 1+3x+10x^2=0
1+3x-10x^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
$$a = -10$$
$$b = 3$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{5}$$
$$x_{2} = \frac{1}{2}$$
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
$$a = -10$$
$$b = 3$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (-10) * (1) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{5}$$
$$x_{2} = \frac{1}{2}$$
Vieta's Theorem
rewrite the equation
$$- 10 x^{2} + \left(3 x + 1\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{10} - \frac{1}{10} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{10}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{10}$$
$$x_{1} x_{2} = - \frac{1}{10}$$
$$- 10 x^{2} + \left(3 x + 1\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{10} - \frac{1}{10} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{10}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{10}$$
$$x_{1} x_{2} = - \frac{1}{10}$$
Sum and product of roots
[src]
sum
-1/5 + 1/2
$$- \frac{1}{5} + \frac{1}{2}$$
=
3/10
$$\frac{3}{10}$$
product
-1 --- 5*2
$$- \frac{1}{10}$$
=
-1/10
$$- \frac{1}{10}$$
-1/10
The graph