Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1-7*(4+2*x)=-9-4*x
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Equation -x-2+3(x-3)=3(4-x)-3
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Equation (x+2)^2=(1-x)^2
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Equation (x-2)^2=(x-9)^2
- Express {x} in terms of y where:
- -14*x-16*y=14
- -6*x-20*y=8
- 17*x-18*y=10
- 9*x-4*y=2
-
Identical expressions
- two 3x^2= zero
- 23x squared equally 0
- two 3x squared equally zero
- 23x2=0
- 23x²=0
- 23x to the power of 2=0
- 23x^2=O
23x^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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
$$a = 23$$
$$b = 0$$
$$c = 0$$
, then
$$D = b^2 - 4\ a\ c = $$
$$0^{2} - 23 \cdot 4 \cdot 0 = 0$$
Because D = 0, then the equation has one root.
$$x_{1} = 0$$
$$a\ x^2 + b\ x + c = 0$$
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
$$a = 23$$
$$b = 0$$
$$c = 0$$
, then
$$D = b^2 - 4\ a\ c = $$
$$0^{2} - 23 \cdot 4 \cdot 0 = 0$$
Because D = 0, then the equation has one root.
x = -b/2a = -0/2/(23)
$$x_{1} = 0$$
Vieta's Theorem
rewrite the equation
$$23 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 0$$
$$23 x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
0
$$\left(0\right)$$
=
0
$$0$$
product
0
$$\left(0\right)$$
=
0
$$0$$
The graph