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One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.
- a)3, –2
- b)–3, 2
- c)–6, –1
- d)6, –1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
One of the two students, while solving a quadratic equation in x, copi...
Let's call the constant term of the quadratic equation "c" and the coefficient of x^2 "a".
The first student copied the constant term incorrectly, so the actual constant term is different from what they wrote down. Let's say they wrote down "k" instead of "c". Therefore, the quadratic equation they solved is ax^2 + bx + k = 0.
The second student copied the constant term and coefficient of x^2 correctly, so the quadratic equation they solved is ax^2 + bx + c = 0.
Since the roots of the quadratic equation are 3 and 2, we can set up the following equations:
For the first student:
a(3)^2 + b(3) + k = 0 (Equation 1)
For the second student:
a(2)^2 + b(2) + c = 0 (Equation 2)
Now, let's solve these equations to find the values of a, b, c, and k.
From Equation 1:
9a + 3b + k = 0 (Equation 3)
From Equation 2:
4a + 2b + c = 0 (Equation 4)
Since the second student copied the constant term and coefficient of x^2 correctly, we can assume that Equation 4 is the correct equation. Therefore, we can rewrite Equation 4 as:
4a + 2b + k = 0 (Equation 5)
Now, we have two equations (Equation 3 and Equation 5) with the same constant term "k". By comparing the coefficients of "a" and "b" in these two equations, we can see that they are the same. Therefore, we can conclude that the constant term copied by the first student is also "c".
In summary, both students copied the constant term and coefficient of x^2 correctly, and the constant term of the quadratic equation is "c".
The first student copied the constant term incorrectly, so the actual constant term is different from what they wrote down. Let's say they wrote down "k" instead of "c". Therefore, the quadratic equation they solved is ax^2 + bx + k = 0.
The second student copied the constant term and coefficient of x^2 correctly, so the quadratic equation they solved is ax^2 + bx + c = 0.
Since the roots of the quadratic equation are 3 and 2, we can set up the following equations:
For the first student:
a(3)^2 + b(3) + k = 0 (Equation 1)
For the second student:
a(2)^2 + b(2) + c = 0 (Equation 2)
Now, let's solve these equations to find the values of a, b, c, and k.
From Equation 1:
9a + 3b + k = 0 (Equation 3)
From Equation 2:
4a + 2b + c = 0 (Equation 4)
Since the second student copied the constant term and coefficient of x^2 correctly, we can assume that Equation 4 is the correct equation. Therefore, we can rewrite Equation 4 as:
4a + 2b + k = 0 (Equation 5)
Now, we have two equations (Equation 3 and Equation 5) with the same constant term "k". By comparing the coefficients of "a" and "b" in these two equations, we can see that they are the same. Therefore, we can conclude that the constant term copied by the first student is also "c".
In summary, both students copied the constant term and coefficient of x^2 correctly, and the constant term of the quadratic equation is "c".
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Community Answer
One of the two students, while solving a quadratic equation in x, copi...
Let the equation be x2 + ax + b = 0
Its roots are 3 and 2
∴ Sum of roots, 5 = –a
and product of roots, 6 = b
∴ Equation is x2 – 5x + 6 = 0
Now constant term is wrong and it is given that correct constant term is – 6.
∴ x2 – 5x – 6 = 0 is the correct equation.
Its roots are –1 and 6.
Its roots are 3 and 2
∴ Sum of roots, 5 = –a
and product of roots, 6 = b
∴ Equation is x2 – 5x + 6 = 0
Now constant term is wrong and it is given that correct constant term is – 6.
∴ x2 – 5x – 6 = 0 is the correct equation.
Its roots are –1 and 6.
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One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer?
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One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer?.
One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.a)3, –2b)–3, 2c)–6, –1d)6, –1Correct answer is option 'D'. Can you explain this answer?.
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