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In this question, two equations are given. Answer the questions based on given equations:
I. 2x2 - Px + 10 = 0
a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b)
II. 4y2 - Ry + 19 = 0
c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d)
Which of the following statements is/are correct?
I. Values of a + c = b + d
II. c + d = 5.75
III. a > b > c > d
- a)Only I
- b)Only III
- c)Only II
- d)All of these
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In this question, two equations are given. Answer the questions based ...
Solution:
I. 2x
2
- Px + 10 = 0a and b are two roots and a + b = 4.5
sum of roots = -(coefficient of x)/(coefficient of x2)
= 4.5 = 9/2
Coefficient of x = 9
P = 9
2x
2
- 9x + 10 = 0
2x
2
- 4x - 5x + 10 = 0
2x(x
- 2) - 5(x - 2) = 0
(x - 2) (2x - 5) = 0
x = 2 and 2.5
a > b
a = 2.5
b = 2
II. 4y
2
- Ry + 19 = 0c and d are two roots of the given equation such as one root is 40% of the largest root of first equation.
one root = 40/100 × 2.5 = 1
Product of roots = constant term/coefficient of y
= 19/4
c × d = 4.75
c > d
c = 4.75
d = 1
Roots of second equation = 1 and 4.75
I. Values of a + c = b + d
LHS, a + c = 2.5 + 4.75 = 7.25
RHS, b + d = 2 + 1 = 3
LHS ≠ RHS
II. c + d = 5.75
LHS, c + d = 4.75 + 1
= 5.75 = RHS
III. a > b > c > d
Incorrect since c have highest value.
Most Upvoted Answer
In this question, two equations are given. Answer the questions based ...
Given Equations
I. 2x2 - Px + 10 = 0
a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b)
II. 4y2 - Ry + 19 = 0
c and d are two roots of the given equation such as one root is 40% of the largest root of the first equation. (c > d)
Analysis
To determine which statements are correct, we need to analyze the information provided in the given equations.
I. Values of a + c = b + d
From the first equation, we know that a + b = 4.5.
From the second equation, let's assume that one root of the second equation (4y2 - Ry + 19 = 0) is 40% of the largest root of the first equation (2x2 - Px + 10 = 0).
Let the largest root of the first equation be 'x1'.
So, one root of the second equation is 0.4 * x1.
Therefore, a + 0.4x1 = b + 0.6x1.
Since a + b = 4.5, we can say that 0.4x1 + 4.5 = 0.6x1 + 4.5.
Solving this, we get x1 = 9 and a = 1.8, b = 2.7.
Now, from the second equation, we can say that c = 0.4 * 9 = 3.6, d = 0.6 * 9 = 5.4.
Therefore, a + c = 1.8 + 3.6 = 5.4 and b + d = 2.7 + 5.4 = 8.1.
So, the statement is incorrect.
Conclusion
The correct statement is:
c) Only II. a > b > c > d.
I. 2x2 - Px + 10 = 0
a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b)
II. 4y2 - Ry + 19 = 0
c and d are two roots of the given equation such as one root is 40% of the largest root of the first equation. (c > d)
Analysis
To determine which statements are correct, we need to analyze the information provided in the given equations.
I. Values of a + c = b + d
From the first equation, we know that a + b = 4.5.
From the second equation, let's assume that one root of the second equation (4y2 - Ry + 19 = 0) is 40% of the largest root of the first equation (2x2 - Px + 10 = 0).
Let the largest root of the first equation be 'x1'.
So, one root of the second equation is 0.4 * x1.
Therefore, a + 0.4x1 = b + 0.6x1.
Since a + b = 4.5, we can say that 0.4x1 + 4.5 = 0.6x1 + 4.5.
Solving this, we get x1 = 9 and a = 1.8, b = 2.7.
Now, from the second equation, we can say that c = 0.4 * 9 = 3.6, d = 0.6 * 9 = 5.4.
Therefore, a + c = 1.8 + 3.6 = 5.4 and b + d = 2.7 + 5.4 = 8.1.
So, the statement is incorrect.
Conclusion
The correct statement is:
c) Only II. a > b > c > d.
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In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer? for Italian 2025 is part of Italian preparation. The Question and answers have been prepared according to the Italian exam syllabus. Information about In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Italian 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer?.
In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer? for Italian 2025 is part of Italian preparation. The Question and answers have been prepared according to the Italian exam syllabus. Information about In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Italian 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In this question, two equations are given. Answer the questions based on given equations: I. 2x2 - Px + 10 = 0 a and b are two roots of the given equation and their sum is a + b = 4.5. (a > b) II. 4y2 - Ry + 19 = 0 c and d are two roots of the given equation such as one root is 40% of the largest root of first equation. (c > d) Which of the following statements is/are correct? I. Values of a + c = b + d II. c + d = 5.75 III. a > b > c > da)Only Ib)Only IIIc)Only IId)All of thesee)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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