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- 5a²+2a=0
5a²-2a=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:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 5$$
$$b = -2$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$a_{1} = \frac{2}{5}$$
$$a_{2} = 0$$
a*a^2 + b*a + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 5$$
$$b = -2$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (5) * (0) = 4
Because D > 0, then the equation has two roots.
a1 = (-b + sqrt(D)) / (2*a)
a2 = (-b - sqrt(D)) / (2*a)
or
$$a_{1} = \frac{2}{5}$$
$$a_{2} = 0$$
Vieta's Theorem
rewrite the equation
$$5 a^{2} - 2 a = 0$$
of
$$a^{3} + a b + c = 0$$
as reduced quadratic equation
$$a^{2} + b + \frac{c}{a} = 0$$
$$a^{2} - \frac{2 a}{5} = 0$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{2}{5}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = \frac{2}{5}$$
$$a_{1} a_{2} = 0$$
$$5 a^{2} - 2 a = 0$$
of
$$a^{3} + a b + c = 0$$
as reduced quadratic equation
$$a^{2} + b + \frac{c}{a} = 0$$
$$a^{2} - \frac{2 a}{5} = 0$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{2}{5}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = \frac{2}{5}$$
$$a_{1} a_{2} = 0$$
Sum and product of roots
[src]
sum
2/5
$$\frac{2}{5}$$
=
2/5
$$\frac{2}{5}$$
product
0*2 --- 5
$$\frac{0 \cdot 2}{5}$$
=
0
$$0$$
0