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Question 1 of 5
If the roots of 2x2−3x−2=0 are α and β, find:
α2+β2
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
Manipulate the given expression until you can substitute the sum and product of roots.
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α2+β2 |
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= |
α2 +2αβ+β2 −2αβ |
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= |
(α+β)2−2αβ |
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= |
(32)2−2(−1) |
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= |
94+2 |
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= |
174 |
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= |
414 |
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Question 2 of 5
If the roots of 2x2−3x−2=0 are α and β, find:
α2β3+β2α3
Write fractions in the format “a/b”
Incorrect
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Progress: 0%
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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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α2β3+β2α3 |
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= |
α2β2(α+β) |
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= |
(αβ)2(α+β) |
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= |
(−1)2(32) |
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= |
1(32) |
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= |
32 |
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Question 3 of 5
If the roots of x2−5x+1=0 are α and β, find:
α2+β2
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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α2+β2 |
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= |
(α+β)2−2αβ |
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= |
(5)2−2(1) |
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= |
25−2 |
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= |
23 |
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Question 4 of 5
If the roots of x2−5x+1=0 are α and β, find:
α2β3+β2α3
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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α2β3+β2α3 |
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= |
α2β2(α+β) |
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= |
(αβ)2(α+β) |
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= |
(1)2(5) |
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= |
5 |
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Question 5 of 5
If the roots of 2x2−4x−1=0 are α and β, find:
α2+β2
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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α2+β2 |
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= |
(α+β)2−2αβ |
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= |
(2)2−2(−12) |
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= |
4+1 |
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= |
5 |