Mister Exam
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- Equation:
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Equation 2*(-4*x^2/(x^2-4)+1+(x^2+4)*(4*x^2/(x^2-4)-1)/(x^2-4))/(x^2-4)=0
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Equation 4(x+6)=x
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Equation x^2-5*x-1=0
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Identical expressions
- 4x^ two −14x+ six = zero
- 4x squared −14x plus 6 equally 0
- 4x to the power of two −14x plus six equally zero
- 4x2−14x+6=0
- 4x²−14x+6=0
- 4x to the power of 2−14x+6=0
- 4x^2−14x+6=O
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Similar expressions
- 4x^2−14x-6=0
4x^2−14x+6=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
$$a = 4$$
$$b = -14$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = \frac{1}{2}$$
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
$$a = 4$$
$$b = -14$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(-14)^2 - 4 * (4) * (6) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = \frac{1}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(4 x^{2} - 14 x\right) + 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7 x}{2} + \frac{3}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{7}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{3}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{7}{2}$$
$$x_{1} x_{2} = \frac{3}{2}$$
$$\left(4 x^{2} - 14 x\right) + 6 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7 x}{2} + \frac{3}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{7}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{3}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{7}{2}$$
$$x_{1} x_{2} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
1/2 + 3
$$\frac{1}{2} + 3$$
=
7/2
$$\frac{7}{2}$$
product
3 - 2
$$\frac{3}{2}$$
=
3/2
$$\frac{3}{2}$$
3/2