Mister Exam
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- (8z+ one)⋅(8z− three)⋅(12z− seventeen)= zero
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Similar expressions
- (8z-1)⋅(8z−3)⋅(12z−17)=0
(8z+1)⋅(8z−3)⋅(12z−17)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(8*z + 1)*(8*z - 3)*(12*z - 17) = 0
$$\left(8 z - 3\right) \left(8 z + 1\right) \left(12 z - 17\right) = 0$$
Detail solution
Given the equation:
$$\left(8 z - 3\right) \left(8 z + 1\right) \left(12 z - 17\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$8 z - 3 = 0$$
$$8 z + 1 = 0$$
$$12 z - 17 = 0$$
solve the resulting equation:
1.
$$8 z - 3 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$8 z = 3$$
Divide both parts of the equation by 8
We get the answer: z1 = 3/8
2.
$$8 z + 1 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$8 z = -1$$
Divide both parts of the equation by 8
We get the answer: z2 = -1/8
3.
$$12 z - 17 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$12 z = 17$$
Divide both parts of the equation by 12
We get the answer: z3 = 17/12
The final answer:
$$z_{1} = \frac{3}{8}$$
$$z_{2} = - \frac{1}{8}$$
$$z_{3} = \frac{17}{12}$$
$$\left(8 z - 3\right) \left(8 z + 1\right) \left(12 z - 17\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$8 z - 3 = 0$$
$$8 z + 1 = 0$$
$$12 z - 17 = 0$$
solve the resulting equation:
1.
$$8 z - 3 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$8 z = 3$$
Divide both parts of the equation by 8
z = 3 / (8)
We get the answer: z1 = 3/8
2.
$$8 z + 1 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$8 z = -1$$
Divide both parts of the equation by 8
z = -1 / (8)
We get the answer: z2 = -1/8
3.
$$12 z - 17 = 0$$
Move free summands (without z)
from left part to right part, we given:
$$12 z = 17$$
Divide both parts of the equation by 12
z = 17 / (12)
We get the answer: z3 = 17/12
The final answer:
$$z_{1} = \frac{3}{8}$$
$$z_{2} = - \frac{1}{8}$$
$$z_{3} = \frac{17}{12}$$
Rapid solution
[src]
z1 = -1/8
$$z_{1} = - \frac{1}{8}$$
z2 = 3/8
$$z_{2} = \frac{3}{8}$$
17
z3 = --
12
$$z_{3} = \frac{17}{12}$$
z3 = 17/12
Sum and product of roots
[src]
sum
17
-1/8 + 3/8 + --
12
$$\left(- \frac{1}{8} + \frac{3}{8}\right) + \frac{17}{12}$$
=
5/3
$$\frac{5}{3}$$
product
-3 ---*17 8*8 ------ 12
$$\frac{17 \left(- \frac{3}{64}\right)}{12}$$
=
-17 ---- 256
$$- \frac{17}{256}$$
-17/256