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If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is?
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If |x³-9x²+26x-24| is a prime no. then the no. of possible integral va...
Solution:
Given expression is |x³-9x²+26x-24|
Let's factorize the expression:
|x³-9x²+26x-24| = |x²(x-9)+2(x-9)|
= |(x-9)(x²+2)|
Now, for the expression to be a prime number, one of the factors must be equal to 1 and the other factor must be the prime number.
Case 1: x-9 = 1
This gives us x = 10
Substituting x = 10 in the expression, we get:
|10²+2| = 102 which is a prime number.
Case 2: x²+2 = 1
This gives us x = ±i√2
However, we are looking for integral values of x, which excludes complex numbers.
Therefore, the only possible value of x is 10.
Conclusion:
The only possible integral value of x that makes the expression a prime number is x = 10.
Given expression is |x³-9x²+26x-24|
Let's factorize the expression:
|x³-9x²+26x-24| = |x²(x-9)+2(x-9)|
= |(x-9)(x²+2)|
Now, for the expression to be a prime number, one of the factors must be equal to 1 and the other factor must be the prime number.
Case 1: x-9 = 1
This gives us x = 10
Substituting x = 10 in the expression, we get:
|10²+2| = 102 which is a prime number.
Case 2: x²+2 = 1
This gives us x = ±i√2
However, we are looking for integral values of x, which excludes complex numbers.
Therefore, the only possible value of x is 10.
Conclusion:
The only possible integral value of x that makes the expression a prime number is x = 10.
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If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is?
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If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is?.
If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |x³-9x²+26x-24| is a prime no. then the no. of possible integral value of x is?.
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