Mister Exam
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Similar expressions
- 4*a*x+x^2=0
4*a*x-x^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
$$a = -1$$
$$b = 4 a$$
$$c = 0$$
, then
The equation has two roots.
or
$$x_{1} = 2 a - 2 \sqrt{a^{2}}$$
Simplify
$$x_{2} = 2 a + 2 \sqrt{a^{2}}$$
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 - it is the discriminant.
Because
$$a = -1$$
$$b = 4 a$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(4*a)^2 - 4 * (-1) * (0) = 16*a^2
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 a - 2 \sqrt{a^{2}}$$
Simplify
$$x_{2} = 2 a + 2 \sqrt{a^{2}}$$
Simplify
Vieta's Theorem
rewrite the equation
$$4 a x - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- 4 a x + x^{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - 4 a$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4 a$$
$$x_{1} x_{2} = 0$$
$$4 a x - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$- 4 a x + x^{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - 4 a$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4 a$$
$$x_{1} x_{2} = 0$$
The graph
Sum and product of roots
[src]
sum
0 + 0 + 4*a
$$4 a + \left(0 + 0\right)$$
=
4*a
$$4 a$$
product
1*0*4*a
$$1 \cdot 0 \cdot 4 a$$
=
0
$$0$$
0