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If x = 3 is 1 solution for the equation 2x2 − 5x − α = 0, what is the value of a?
- a)−2
- b)0
- c)3
- d)5
- e)6
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If x = 3 is 1 solution for the equation 2x2 − 5x − α...
Given:
x = 3 is a solution for the equation 2x^2 - 5x - α = 0
To Find:
The value of α
Solution:
- Substitute x = 3 into the equation:
2(3)^2 - 5(3) - α = 0
18 - 15 - α = 0
3 - α = 0
- Solve for α:
α = 3
Therefore, the value of α is 3, which corresponds to option C.
Community Answer
If x = 3 is 1 solution for the equation 2x2 − 5x − α...
The correct answer is C. You are given that x = 3 is one solution, which means that (x − 3) is one of the factors of 2x2 − 5x − α = 0. Since the coefficient of the x2 –term is 2, you can set up the other factors as follows: (2x +__)(x − 3)
The x terms must equal –5, so apply the FOIL method to find the missing term:
−6x + x = −5x
−6x + x = −5x; the missing term must be 1.
Use FOIL again to solve for α:
(2x + 1)(x − 3)
2x2 − 6x + x − 3
2x2 − 5x − 3
Thus, α = 3.
The x terms must equal –5, so apply the FOIL method to find the missing term:
−6x + x = −5x
−6x + x = −5x; the missing term must be 1.
Use FOIL again to solve for α:
(2x + 1)(x − 3)
2x2 − 6x + x − 3
2x2 − 5x − 3
Thus, α = 3.
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If x = 3 is 1 solution for the equation 2x2 − 5x − α = 0, what is the value of a?a)−2b)0c)3d)5e)6Correct answer is option 'C'. Can you explain this answer?
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