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Question 1 of 5
If the roots of 2x2-3x-2=02x2−3x−2=0 are αα and ββ, find:
(α-2)(β-2)(α−2)(β−2)
Incorrect
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First, list the coefficients of the quadratic equation individually
Slot the coefficients to the Sum and Product of Roots Formula
α+βα+β |
== |
−ba−ba |
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== |
−−32−−32 |
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== |
3232 |
αβαβ |
== |
caca |
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== |
−22−22 |
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== |
-1−1 |
Manipulate the given expression until you can substitute the sum and product of roots.
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(α-2)(β-2)(α−2)(β−2) |
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== |
αβ-2α-2β+4αβ−2α−2β+4 |
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== |
αβ-2(α+β)+4αβ−2(α+β)+4 |
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== |
(-1)-2(32)+4(−1)−2(32)+4 |
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== |
-1-3+4−1−3+4 |
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== |
00 |
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Question 2 of 5
If the roots of x2-5x+1=0x2−5x+1=0 are αα and ββ, find:
4α+4β4α+4β
Incorrect
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Progress: 0%
0:00
First, list the coefficients of the quadratic equation individually
Slot the coefficients to the Sum and Product of Roots Formula
α+βα+β |
== |
−ba−ba |
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== |
−−51−−51 |
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== |
55 |
αβαβ |
== |
caca |
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== |
1111 |
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== |
11 |
Manipulate the given expression until you can substitute the sum and product of roots.
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4α+4β4α+4β |
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== |
4α+4βαβ4α+4βαβ |
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== |
4(α+β)αβ4(α+β)αβ |
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== |
4(5)14(5)1 |
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== |
2020 |
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Question 3 of 5
If the roots of x2-5x+1=0x2−5x+1=0 are αα and ββ, find:
(α-3)(β-3)(α−3)(β−3)
Incorrect
Loaded: 0%
Progress: 0%
0:00
First, list the coefficients of the quadratic equation individually
Slot the coefficients to the Sum and Product of Roots Formula
α+βα+β |
== |
−ba−ba |
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|
== |
−−51−−51 |
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|
== |
55 |
αβαβ |
== |
caca |
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== |
1111 |
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== |
11 |
Manipulate the given expression until you can substitute the sum and product of roots.
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(α-3)(β-3)(α−3)(β−3) |
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== |
αβ-3α-3β+9αβ−3α−3β+9 |
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== |
αβ-3(α+β)+9αβ−3(α+β)+9 |
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== |
1-3(5)+91−3(5)+9 |
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== |
1-15+91−15+9 |
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== |
-5−5 |
(α-3)(β-3)=-5(α−3)(β−3)=−5
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Question 4 of 5
If the roots of 2x2-4x-1=02x2−4x−1=0 are α and β, find:
1α+1β
Incorrect
Loaded: 0%
Progress: 0%
0:00
First, list the coefficients of the quadratic equation individually
Slot the coefficients to the Sum and Product of Roots Formula
Manipulate the given expression until you can substitute the sum and product of roots.
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1α+1β |
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= |
α+βαβ |
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= |
2-12 |
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= |
-4 |
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Question 5 of 5
If the roots of 2x2-4x-1=0 are α and β, find:
αβ+βα
Incorrect
Loaded: 0%
Progress: 0%
0:00
First, list the coefficients of the quadratic equation individually
Slot the coefficients to the Sum and Product of Roots Formula
Manipulate the given expression until you can substitute the sum and product of roots.
Remember from the previous question that α2+β2=5
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αβ+βα |
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= |
α2+β2αβ |
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= |
5-12 |
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= |
-10 |