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Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.
- a)-9 and 1
- b)9 and -1
- c)9 and 1
- d)8 and 1
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Rocky and Anthony are solving a quadratic equation. While solving, Roc...
To solve this problem, let's first understand the correct method of solving a quadratic equation.
A quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is used to find the roots of a quadratic equation:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's analyze the mistakes made by Rocky and Anthony and find the correct roots.
Mistake made by Rocky:
Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. This means that he mistakenly solved the equation as:
ax^2 + bx + 8 = 0 and ax^2 + bx + 2 = 0
Mistake made by Anthony:
Anthony commits a mistake in the coefficient of x and finds the roots to be -9 and -1. This means that he mistakenly solved the equation as:
ax^2 - 9x + c = 0 and ax^2 - x + c = 0
Finding the correct equation:
To find the correct equation, we need to compare the given roots with the quadratic formula and identify the correct values of a, b, and c.
Comparing the given roots with the quadratic formula:
For the roots to be 8 and 2:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of the roots:
8 = (-b ± √(b^2 - 4ac)) / (2a)
2 = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the equations, we can see that the value of a is the same in both equations, but the values of b and c are different. Therefore, the correct equation is:
ax^2 + bx + c = 0
Similarly, for the roots to be -9 and -1:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of the roots:
-9 = (-b ± √(b^2 - 4ac)) / (2a)
-1 = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the equations, we can see that the value of a is the same in both equations, but the values of b and c are different. Therefore, the correct equation is:
ax^2 + bx + c = 0
Finding the correct roots:
Now that we have found the correct equation, we can solve it using the quadratic formula to find the correct roots.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation with the quadratic formula, we can determine the values of a, b, and c.
Thus, the correct roots of the quadratic equation are 9 and 1, which is option C.
A quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is used to find the roots of a quadratic equation:
x = (-b ± √(b^2 - 4ac)) / (2a)
Now, let's analyze the mistakes made by Rocky and Anthony and find the correct roots.
Mistake made by Rocky:
Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. This means that he mistakenly solved the equation as:
ax^2 + bx + 8 = 0 and ax^2 + bx + 2 = 0
Mistake made by Anthony:
Anthony commits a mistake in the coefficient of x and finds the roots to be -9 and -1. This means that he mistakenly solved the equation as:
ax^2 - 9x + c = 0 and ax^2 - x + c = 0
Finding the correct equation:
To find the correct equation, we need to compare the given roots with the quadratic formula and identify the correct values of a, b, and c.
Comparing the given roots with the quadratic formula:
For the roots to be 8 and 2:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of the roots:
8 = (-b ± √(b^2 - 4ac)) / (2a)
2 = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the equations, we can see that the value of a is the same in both equations, but the values of b and c are different. Therefore, the correct equation is:
ax^2 + bx + c = 0
Similarly, for the roots to be -9 and -1:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of the roots:
-9 = (-b ± √(b^2 - 4ac)) / (2a)
-1 = (-b ± √(b^2 - 4ac)) / (2a)
By comparing the equations, we can see that the value of a is the same in both equations, but the values of b and c are different. Therefore, the correct equation is:
ax^2 + bx + c = 0
Finding the correct roots:
Now that we have found the correct equation, we can solve it using the quadratic formula to find the correct roots.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation with the quadratic formula, we can determine the values of a, b, and c.
Thus, the correct roots of the quadratic equation are 9 and 1, which is option C.
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Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer?
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Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer?.
Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer?.
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Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Rocky and Anthony are solving a quadratic equation. While solving, Rocky commits a mistake in the constant term and finds the roots to be 8 and 2. Anthony commits a mistake in the coefficient of X and finds the roots to be -9 and -1. Find the correct roots.a)-9 and 1b)9 and -1c)9 and 1d)8 and 1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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