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For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reciprocals of its roots?
- a)2/3
- b)-2/3
- c)-3/2
- d)3/2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reci...
We know that if α and β are roots of a quadratic equation then the quadratic equation is of the form
x2 – (α + β) x + αβ = 0
So in the question, α + β = 3 and αβ = 2
Sum of the reciprocals of roots = 
Most Upvoted Answer
For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reci...
To find the sum of the reciprocals of the roots of the quadratic equation x^2 - 3x + 2 = 0, we first need to find the roots of the equation. We can do this by factoring or by using the quadratic formula.
1. Factoring:
The given equation can be factored as (x - 2)(x - 1) = 0.
Setting each factor equal to zero, we get x - 2 = 0 and x - 1 = 0.
Solving for x, we find the roots as x = 2 and x = 1.
2. Quadratic Formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation x^2 - 3x + 2 = 0, we have a = 1, b = -3, and c = 2.
Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(1)(2))) / (2(1))
Simplifying further, we have:
x = (3 ± √(9 - 8)) / 2
x = (3 ± √1) / 2
x = (3 ± 1) / 2
This gives us two possible roots: x = 2 and x = 1.
Now that we have found the roots of the quadratic equation as x = 2 and x = 1, we can find the sum of their reciprocals.
Reciprocal of a number x is 1/x.
The sum of the reciprocals of the roots is given by:
1/2 + 1/1 = 1/2 + 2/2 = 3/2
Therefore, the correct answer is option D) 3/2.
1. Factoring:
The given equation can be factored as (x - 2)(x - 1) = 0.
Setting each factor equal to zero, we get x - 2 = 0 and x - 1 = 0.
Solving for x, we find the roots as x = 2 and x = 1.
2. Quadratic Formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation x^2 - 3x + 2 = 0, we have a = 1, b = -3, and c = 2.
Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(1)(2))) / (2(1))
Simplifying further, we have:
x = (3 ± √(9 - 8)) / 2
x = (3 ± √1) / 2
x = (3 ± 1) / 2
This gives us two possible roots: x = 2 and x = 1.
Now that we have found the roots of the quadratic equation as x = 2 and x = 1, we can find the sum of their reciprocals.
Reciprocal of a number x is 1/x.
The sum of the reciprocals of the roots is given by:
1/2 + 1/1 = 1/2 + 2/2 = 3/2
Therefore, the correct answer is option D) 3/2.
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For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reciprocals of its roots?a)2/3b)-2/3c)-3/2d)3/2Correct answer is option 'D'. Can you explain this answer?
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For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reciprocals of its roots?a)2/3b)-2/3c)-3/2d)3/2Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reciprocals of its roots?a)2/3b)-2/3c)-3/2d)3/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the quadratic equation x2 -3x + 2 = 0, what is the sum of the reciprocals of its roots?a)2/3b)-2/3c)-3/2d)3/2Correct answer is option 'D'. Can you explain this answer?.
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