Answer:
See below.
Step-by-step explanation:
(a) Because the solution led to a square root of a negative number:
x^2 -10x+40=0
x^2 - 10x = -40 Completing the square:
(x - 5)^2 - 25 = -40
(x - 5)^2 = -15
x = 5 +/-√(-15)
There is no real square root of -15.
(b) A solution was found by introducing the operator i which stands for the square root of -1.
So the solution is
= 5 +/- √(15) i.
These are called complex roots.
(c) Substituting in the original equation:
x^2 - 10 + 40:
((5 + √(-15)i)^2 - 10(5 + √(-15)i) + 40
= 25 + 10√(-15)i - 15 - 50 - 10√(-15)i + 40
= 25 - 15 - 50 + 40
= 0. So this checks out.
Now substitute 5 - √(-15)i
= 25 - 10√(-15)i - 15 - 50 + 10√(-15)i + 40
= 25 - 15 - 50 + 40
= 0. This checks out also.
Answer:
2
Step-by-step explanation:
roots are the intercepts at the x axis I believe
3(k-x)= -3x-9
3k - 3x = -3x - 9 ← equation without parentheses
3k - 3x + 3x = - 9
3k = -9
k = -9/3
k = -3 ← simplest form
Answer: 3/1=3
18/6=3
-6/-2=3
-15/-5=3
they all have the same quotient
Answer:
a) -8, -6, -1, 5,8
Step-by-step explanation:
*View the image attached*
- As you can see, the further left on the number line, the smaller the number becomes.
- The further right on the number line, the bigger the number becomes.
Hope this helps!
