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Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are
- a)9, 1
- b)-9, 1
- c)9, -1
- d)-9, -1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Mohan and Sohan solve an equation. In solving Mohan commits a mistake...
Correct sum = 8 + 2 = 10 from Mohan
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Correct product = -9 x -1 = 9 from Sohan
∴ x2 – (10)x + 9 = 0
⇒ x2 – 10x + 9 = 0
⇒ x2 – 9x – x + 9
⇒ x(x – 9) – 1(x – 9) = 0
⇒ (x - 9) (x -1) = 0 .
⇒ Correct roots are 9 and 1.
Most Upvoted Answer
Mohan and Sohan solve an equation. In solving Mohan commits a mistake...
Given information:
- Mohan made a mistake in the constant term and got roots 8 and 2.
- Sohan made a mistake in the coefficient of x.
Let's denote the correct roots as a and b.
Mistake in constant term
If Mohan made a mistake in the constant term, it means he changed the constant term from c to k.
The equation with roots 8 and 2 can be written as:
(x - 8)(x - 2) = 0
Expanding this equation, we get:
x^2 - 10x + 16 = 0
But Mohan made a mistake in the constant term, so he wrote the equation as:
x^2 - 10x + k = 0
Let's find the value of k.
We know that the sum of roots of a quadratic equation is -b/a.
So, a+b = 10/1 = 10
We also know that the product of roots of a quadratic equation is c/a.
So, ab = 16/1 = 16
Using these two equations, we can find the value of k as follows:
(x-a)(x-b) = x^2 - (a+b)x + ab = x^2 - 10x + 16
So, k = ab = 16
Therefore, the equation with the correct constant term is:
x^2 - 10x + 16 = 0
Mistake in coefficient of x
If Sohan made a mistake in the coefficient of x, it means he changed the coefficient from 1 to -1.
The equation with correct roots a and b can be written as:
(x - a)(x - b) = 0
If we expand this equation, we get:
x^2 - (a+b)x + ab = 0
But Sohan made a mistake in the coefficient of x, so he wrote the equation as:
-x^2 + (a+b)x - ab = 0
Let's find the roots of this equation using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = (a+b), and c = -ab
Substituting the values of a, b, and c, we get:
x = (-(a+b) ± sqrt((a+b)^2 + 4ab)) / 2(-1)
Simplifying this expression, we get:
x = (-(a+b) ± sqrt((a-b)^2)) / 2
Since the discriminant is zero, the roots are real and equal.
So, we have:
-(a+b) ± (a-b) = 0
Solving these two equations, we get:
a = 9 and b = 1
Therefore, the correct roots are 9 and 1, which is option A.
- Mohan made a mistake in the constant term and got roots 8 and 2.
- Sohan made a mistake in the coefficient of x.
Let's denote the correct roots as a and b.
Mistake in constant term
If Mohan made a mistake in the constant term, it means he changed the constant term from c to k.
The equation with roots 8 and 2 can be written as:
(x - 8)(x - 2) = 0
Expanding this equation, we get:
x^2 - 10x + 16 = 0
But Mohan made a mistake in the constant term, so he wrote the equation as:
x^2 - 10x + k = 0
Let's find the value of k.
We know that the sum of roots of a quadratic equation is -b/a.
So, a+b = 10/1 = 10
We also know that the product of roots of a quadratic equation is c/a.
So, ab = 16/1 = 16
Using these two equations, we can find the value of k as follows:
(x-a)(x-b) = x^2 - (a+b)x + ab = x^2 - 10x + 16
So, k = ab = 16
Therefore, the equation with the correct constant term is:
x^2 - 10x + 16 = 0
Mistake in coefficient of x
If Sohan made a mistake in the coefficient of x, it means he changed the coefficient from 1 to -1.
The equation with correct roots a and b can be written as:
(x - a)(x - b) = 0
If we expand this equation, we get:
x^2 - (a+b)x + ab = 0
But Sohan made a mistake in the coefficient of x, so he wrote the equation as:
-x^2 + (a+b)x - ab = 0
Let's find the roots of this equation using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = (a+b), and c = -ab
Substituting the values of a, b, and c, we get:
x = (-(a+b) ± sqrt((a+b)^2 + 4ab)) / 2(-1)
Simplifying this expression, we get:
x = (-(a+b) ± sqrt((a-b)^2)) / 2
Since the discriminant is zero, the roots are real and equal.
So, we have:
-(a+b) ± (a-b) = 0
Solving these two equations, we get:
a = 9 and b = 1
Therefore, the correct roots are 9 and 1, which is option A.
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Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots area)9, 1b)-9, 1c)9, -1d)-9, -1Correct answer is option 'A'. Can you explain this answer?
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Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots area)9, 1b)-9, 1c)9, -1d)-9, -1Correct answer is option 'A'. 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 Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots area)9, 1b)-9, 1c)9, -1d)-9, -1Correct answer is option 'A'. 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 Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots area)9, 1b)-9, 1c)9, -1d)-9, -1Correct answer is option 'A'. Can you explain this answer?.
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