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Find the minimum value of the quadratic expression 3x2 + 11x - 23.
- a)-23
- b)0
- c)17/12
- d)-397/12
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-2...
The minimum value of a quadratic expression ax2 + bx + c (when a > 0) occurs at x = -b / 2a and its minimum value is -(b2 - 4ac) / 4a
The minimum value of the equation is = [4(3)(-23) - (11)2]/12 = -397 / 12
Hence, option 4.
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Community Answer
Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-2...
To find the minimum value of the quadratic expression 3x^2 + 11x - 23, we can use the concept of the vertex of a parabola. The vertex represents the minimum or maximum point of the quadratic function.
The formula for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by:
x = -b/2a
In this case, a = 3 and b = 11. Substituting these values into the formula, we get:
x = -11 / (2 * 3)
x = -11/6
Now, to find the minimum value of the expression, we substitute this value of x back into the quadratic function:
3(-11/6)^2 + 11(-11/6) - 23
Simplifying this expression, we get:
3(121/36) - 121/6 - 23
363/36 - 242/36 - 23
(363 - 242 - 828) / 36
-707/36
Therefore, the minimum value of the quadratic expression 3x^2 + 11x - 23 is -707/36, which is approximately -19.64.
So, the correct answer is option D) -397/12.
The formula for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by:
x = -b/2a
In this case, a = 3 and b = 11. Substituting these values into the formula, we get:
x = -11 / (2 * 3)
x = -11/6
Now, to find the minimum value of the expression, we substitute this value of x back into the quadratic function:
3(-11/6)^2 + 11(-11/6) - 23
Simplifying this expression, we get:
3(121/36) - 121/6 - 23
363/36 - 242/36 - 23
(363 - 242 - 828) / 36
-707/36
Therefore, the minimum value of the quadratic expression 3x^2 + 11x - 23 is -707/36, which is approximately -19.64.
So, the correct answer is option D) -397/12.
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Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer?.
Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the minimum value of the quadratic expression 3x2 + 11x - 23.a)-23b)0c)17/12d)-397/12Correct answer is option 'D'. Can you explain this answer?.
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