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x2 - 2ax + b = 0
In the equation above, a and b are constants. If this equation is solved for x, there are two solutions. What is the sum of these two solutions?
In the equation above, a and b are constants. If this equation is solved for x, there are two solutions. What is the sum of these two solutions?
- a)2a
- b)-2a
- c)b
- d)-b
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
x2 - 2ax + b = 0In the equation above, a and b are constants. If this ...
That the solutions to quadratic of the form x2 + bx + c = 0, the sum of those solutions is - b (the opposite of whatever the x coefficient is), and the product of those solutions is c (whatever the constant term is). In the quadratic x2 - 2ax + b = 0, the x coefficient is -2a. Since this must be the opposite of the sum of the solutions, the sum of the solutions is 2a.
Although using this theorem gives us a quick and easy solution, the theorem may seem a little abstract and mysterious to you. So, there is another way to attack this question: just choose values of a and b so that the quadratic is easy to factor. For instance, if we choose a = 1 and b = -3, we get:
x2 - 2(1)x - 3 = 0
Simplify: x2 - 2x - 3 = 0
Factor: (x - 3)(x + 1) = 0
Solve with the Zero Product Property: x = 3 or -1
The sum of these two solutions is 3 + -1 = 2.
Now we plug a = 1 and b = -3 into the answer choices and we get (A) 2, (B) -2, (C) -3, (D) 3. Clearly, the only choice that gives the correct sum is (A).
Although using this theorem gives us a quick and easy solution, the theorem may seem a little abstract and mysterious to you. So, there is another way to attack this question: just choose values of a and b so that the quadratic is easy to factor. For instance, if we choose a = 1 and b = -3, we get:
x2 - 2(1)x - 3 = 0
Simplify: x2 - 2x - 3 = 0
Factor: (x - 3)(x + 1) = 0
Solve with the Zero Product Property: x = 3 or -1
The sum of these two solutions is 3 + -1 = 2.
Now we plug a = 1 and b = -3 into the answer choices and we get (A) 2, (B) -2, (C) -3, (D) 3. Clearly, the only choice that gives the correct sum is (A).
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x2 - 2ax + b = 0In the equation above, a and b are constants. If this equation is solved for x, there are two solutions. What is the sum of these two solutions?a)2ab)-2ac)bd)-bCorrect answer is option 'A'. Can you explain this answer?
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