Mister Exam
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Identical expressions
- (S+ three , twenty-four)(23s+ one)
- (S plus 3,24)(23s plus 1)
- (S plus three , twenty minus four)(23s plus one)
- S+3,2423s+1
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Similar expressions
- (S-3,24)(23s+1)
- (S+3,24)(23s-1)
(S+3,24)(23s+1) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 81\ |s + --|*(23*s + 1) = 0 \ 25/
$$\left(s + \frac{81}{25}\right) \left(23 s + 1\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(s + \frac{81}{25}\right) \left(23 s + 1\right) = 0$$
We get the quadratic equation
$$23 s^{2} + \frac{1888 s}{25} + \frac{81}{25} = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$s_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$s_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 23$$
$$b = \frac{1888}{25}$$
$$c = \frac{81}{25}$$
, then
Because D > 0, then the equation has two roots.
or
$$s_{1} = - \frac{1}{23}$$
$$s_{2} = - \frac{81}{25}$$
$$\left(s + \frac{81}{25}\right) \left(23 s + 1\right) = 0$$
We get the quadratic equation
$$23 s^{2} + \frac{1888 s}{25} + \frac{81}{25} = 0$$
This equation is of the form
a*s^2 + b*s + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$s_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$s_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 23$$
$$b = \frac{1888}{25}$$
$$c = \frac{81}{25}$$
, then
D = b^2 - 4 * a * c =
(1888/25)^2 - 4 * (23) * (81/25) = 3378244/625
Because D > 0, then the equation has two roots.
s1 = (-b + sqrt(D)) / (2*a)
s2 = (-b - sqrt(D)) / (2*a)
or
$$s_{1} = - \frac{1}{23}$$
$$s_{2} = - \frac{81}{25}$$
Rapid solution
[src]
-81
s1 = ----
25
$$s_{1} = - \frac{81}{25}$$
s2 = -1/23
$$s_{2} = - \frac{1}{23}$$
s2 = -1/23
Sum and product of roots
[src]
sum
81 - -- - 1/23 25
$$- \frac{81}{25} - \frac{1}{23}$$
=
-1888 ------ 575
$$- \frac{1888}{575}$$
product
-81*(-1) -------- 25*23
$$- \frac{-81}{575}$$
=
81 --- 575
$$\frac{81}{575}$$
81/575