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If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?
- a)Both 21 and 29
- b)Both 26 and 28
- c)Both 22 and 25
- d)All 19, 26 and 30
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the roots of the equation 6x2 - 25x + p = 0 are real and different...
Since, the roots of equation 6x2 - 25x + p = 0 are real and different. So, its discriminant should be positive.
b2 - 4ac > 0
b2 > 4ac
(-25)2 > 4 * 6 * p
625 > 24p
p < />
p < />
Since the value of p is any integer greater than 18 and less than 26.
So, the possible values of p = 19, 20, 21, 22, 23, 24, 25 and 26.
Most Upvoted Answer
If the roots of the equation 6x2 - 25x + p = 0 are real and different...
Real and Different Roots of the Quadratic Equation
In order for the roots of a quadratic equation to be real and different, the discriminant of the quadratic equation should be greater than zero. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Finding the Value of 'p'
Given the quadratic equation 6x^2 - 25x + p = 0, we can compare it with the standard form ax^2 + bx + c = 0 to find the values of a, b, and c. In this case, a = 6, b = -25, and c = p.
Calculating the Discriminant
Substitute the values of a, b, and c into the discriminant formula:
Discriminant = (-25)^2 - 4*6*p
Discriminant = 625 - 24p
For Real and Different Roots
For the roots to be real and different, the discriminant should be greater than zero:
625 - 24p > 0
24p < />
p < />
p < />
Checking the Values of 'p'
Given that p is an integer greater than 18, we need to find the integer values of p that satisfy the condition p < 26="" and="" p="" /> 18.
Therefore, the values of 'p' that satisfy the conditions are:
- 19
- 22
- 25
Hence, the correct answer is option 'C' - Both 22 and 25.
In order for the roots of a quadratic equation to be real and different, the discriminant of the quadratic equation should be greater than zero. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Finding the Value of 'p'
Given the quadratic equation 6x^2 - 25x + p = 0, we can compare it with the standard form ax^2 + bx + c = 0 to find the values of a, b, and c. In this case, a = 6, b = -25, and c = p.
Calculating the Discriminant
Substitute the values of a, b, and c into the discriminant formula:
Discriminant = (-25)^2 - 4*6*p
Discriminant = 625 - 24p
For Real and Different Roots
For the roots to be real and different, the discriminant should be greater than zero:
625 - 24p > 0
24p < />
p < />
p < />
Checking the Values of 'p'
Given that p is an integer greater than 18, we need to find the integer values of p that satisfy the condition p < 26="" and="" p="" /> 18.
Therefore, the values of 'p' that satisfy the conditions are:
- 19
- 22
- 25
Hence, the correct answer is option 'C' - Both 22 and 25.
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If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer?
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If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer?.
If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 6x2 - 25x + p = 0 are real and different, then what can be the value of 'p' if the value of p is any integer greater than 18?a)Both 21 and 29b)Both 26 and 28c)Both 22 and 25d)All 19, 26 and 30Correct answer is option 'C'. Can you explain this answer?.
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