Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=12
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Equation 12-x^2=11
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Equation -sin(x)=0
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Equation 4x+5=2x-7
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- -5*x-6*y=-1
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Identical expressions
- 6x^ two -35x+ fifty = zero
- 6x squared minus 35x plus 50 equally 0
- 6x to the power of two minus 35x plus fifty equally zero
- 6x2-35x+50=0
- 6x²-35x+50=0
- 6x to the power of 2-35x+50=0
- 6x^2-35x+50=O
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Similar expressions
- 6x^2-35x-50=0
- 6x^2+35x+50=0
6x^2-35x+50=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 6$$
$$b = -35$$
$$c = 50$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 6 \cdot 4 \cdot 50 + \left(-35\right)^{2} = 25$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = \frac{10}{3}$$
Simplify
$$x_{2} = \frac{5}{2}$$
Simplify
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 6$$
$$b = -35$$
$$c = 50$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 6 \cdot 4 \cdot 50 + \left(-35\right)^{2} = 25$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = \frac{10}{3}$$
Simplify
$$x_{2} = \frac{5}{2}$$
Simplify
Vieta's Theorem
rewrite the equation
$$6 x^{2} - 35 x + 50 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{35 x}{6} + \frac{25}{3} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{35}{6}$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{35}{6}$$
$$x_{1} x_{2} = \frac{25}{3}$$
$$6 x^{2} - 35 x + 50 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{35 x}{6} + \frac{25}{3} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{35}{6}$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{35}{6}$$
$$x_{1} x_{2} = \frac{25}{3}$$
Sum and product of roots
[src]
sum
5/2 + 10/3
$$\left(\frac{5}{2}\right) + \left(\frac{10}{3}\right)$$
=
35/6
$$\frac{35}{6}$$
product
5/2 * 10/3
$$\left(\frac{5}{2}\right) * \left(\frac{10}{3}\right)$$
=
25/3
$$\frac{25}{3}$$
The graph