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If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the average (arithmetic mean) of the roots of the equation x2 + 28x – 588 = 0, what is the other root of the equation x2 + bx + 98 = 0?
- a)-7
- b)−5/2
- c)5/2
- d)7
- e)21
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the ...
Given
To Find: value of n?
Approach
- We know that the product of roots m and n is equal to c/a
- So, we can write m*n = 98, i.e. n = 98/m
- So, for finding n, we need to find m
- We are given that m = (p+q)/2
- We know that sum of roots of the quadratic equation is −b/a
- We will use this relation to find the value of p + q and hence the value of m
Hence, the other root of the equation x2 + bx + 98 = 0 is -7
Answer: A
Most Upvoted Answer
If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the ...
Problem Analysis:
We are given two quadratic equations: x^2 + bx + 98 = 0 and x^2 + 28x + 588 = 0. We need to find the other root of the equation x^2 + bx + 98 = 0, given that one of the roots is the average of the roots of the equation x^2 + 28x + 588 = 0.
Key Observations:
Let's denote the roots of x^2 + 28x + 588 = 0 as α and β.
The sum of the roots, α + β, can be found using the formula: α + β = -b/a.
The product of the roots, α * β, can be found using the formula: α * β = c/a.
Solution:
1. Find the sum and product of the roots of x^2 + 28x + 588 = 0:
- Using the formula α + β = -b/a, we find: α + β = -28/1 = -28.
- Using the formula α * β = c/a, we find: α * β = 588/1 = 588.
2. Find the average of the roots of x^2 + 28x + 588 = 0:
- The average of the roots is (α + β)/2 = (-28)/2 = -14.
3. Set up the equation for the other root of x^2 + bx + 98 = 0:
- We know that one of the roots is -14.
- Let the other root be r.
- The sum of the roots is -14 + r = -b/a.
- The product of the roots is -14 * r = 98/a.
4. Solve the equation to find r:
- Rearrange the equation -14 + r = -b/a to get r = -14 - b/a.
- Substitute the value of α * β = 98/a from step 3: -14 * r = 98/a.
- Simplify: -14r = 98/a.
- Multiply both sides by -a/14: r = -98/14 = -7.
5. Answer:
- The other root of the equation x^2 + bx + 98 = 0 is -7.
- Therefore, the correct answer is option A.
We are given two quadratic equations: x^2 + bx + 98 = 0 and x^2 + 28x + 588 = 0. We need to find the other root of the equation x^2 + bx + 98 = 0, given that one of the roots is the average of the roots of the equation x^2 + 28x + 588 = 0.
Key Observations:
Let's denote the roots of x^2 + 28x + 588 = 0 as α and β.
The sum of the roots, α + β, can be found using the formula: α + β = -b/a.
The product of the roots, α * β, can be found using the formula: α * β = c/a.
Solution:
1. Find the sum and product of the roots of x^2 + 28x + 588 = 0:
- Using the formula α + β = -b/a, we find: α + β = -28/1 = -28.
- Using the formula α * β = c/a, we find: α * β = 588/1 = 588.
2. Find the average of the roots of x^2 + 28x + 588 = 0:
- The average of the roots is (α + β)/2 = (-28)/2 = -14.
3. Set up the equation for the other root of x^2 + bx + 98 = 0:
- We know that one of the roots is -14.
- Let the other root be r.
- The sum of the roots is -14 + r = -b/a.
- The product of the roots is -14 * r = 98/a.
4. Solve the equation to find r:
- Rearrange the equation -14 + r = -b/a to get r = -14 - b/a.
- Substitute the value of α * β = 98/a from step 3: -14 * r = 98/a.
- Simplify: -14r = 98/a.
- Multiply both sides by -a/14: r = -98/14 = -7.
5. Answer:
- The other root of the equation x^2 + bx + 98 = 0 is -7.
- Therefore, the correct answer is option A.
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If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the average (arithmetic mean) of the roots of the equation x2 + 28x – 588 = 0, what is the other root of the equation x2 + bx + 98 = 0?a)-7b)−5/2c)5/2d)7e)21Correct answer is option 'A'. Can you explain this answer?
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If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the average (arithmetic mean) of the roots of the equation x2 + 28x – 588 = 0, what is the other root of the equation x2 + bx + 98 = 0?a)-7b)−5/2c)5/2d)7e)21Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the average (arithmetic mean) of the roots of the equation x2 + 28x – 588 = 0, what is the other root of the equation x2 + bx + 98 = 0?a)-7b)−5/2c)5/2d)7e)21Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the roots of the quadratic equation x2 + bx + 98 = 0 is the average (arithmetic mean) of the roots of the equation x2 + 28x – 588 = 0, what is the other root of the equation x2 + bx + 98 = 0?a)-7b)−5/2c)5/2d)7e)21Correct answer is option 'A'. Can you explain this answer?.
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