Mister Exam
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How to use it?
- Equation:
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Equation 2x-3(x+3)=-5
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Equation x^2-4x+4=0
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Equation sin(x)=1/5
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Equation x^2+3x+2=0
- Express {x} in terms of y where:
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Identical expressions
- 7x^ two - twenty-one = zero
- 7x squared minus 21 equally 0
- 7x to the power of two minus twenty minus one equally zero
- 7x2-21=0
- 7x²-21=0
- 7x to the power of 2-21=0
- 7x^2-21=O
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Similar expressions
- 7x^2+21=0
7x^2-21=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
$$a = 7$$
$$b = 0$$
$$c = -21$$
, then
$$D = b^2 - 4\ a\ c = $$
$$0^{2} - 7 \cdot 4 \left(-21\right) = 588$$
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
$$x_{1} = \sqrt{3}$$
Simplify
$$x_{2} = - \sqrt{3}$$
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
$$a = 7$$
$$b = 0$$
$$c = -21$$
, then
$$D = b^2 - 4\ a\ c = $$
$$0^{2} - 7 \cdot 4 \left(-21\right) = 588$$
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
$$x_{1} = \sqrt{3}$$
Simplify
$$x_{2} = - \sqrt{3}$$
Simplify
Vieta's Theorem
rewrite the equation
$$7 x^{2} - 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -3$$
$$7 x^{2} - 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -3$$
Sum and product of roots
[src]
sum
___ ___ -\/ 3 + \/ 3
$$\left(- \sqrt{3}\right) + \left(\sqrt{3}\right)$$
=
0
$$0$$
product
___ ___ -\/ 3 * \/ 3
$$\left(- \sqrt{3}\right) * \left(\sqrt{3}\right)$$
=
-3
$$-3$$
The graph