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If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is?
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If one root of the equation X square - 8 x + k is equal to zero exceed...
Explanation:
Given:
Let the roots of the equation X^2 - 8x + k = 0 be α and β.
Given that one root exceeds the other by 4, we can write the following relationship:
α - β = 4
Now, we know that the sum of the roots of a quadratic equation is given by:
α + β = -(-8) = 8
Using the sum and difference of roots formulas, we can find the individual values of α and β.
Calculations:
- From α + β = 8 and α - β = 4, we get:
2α = 12
α = 6
Substitute α = 6 into α + β = 8:
6 + β = 8
β = 2
Now, using the product of roots formula for a quadratic equation:
α * β = k
6 * 2 = k
k = 12
Therefore, the value of k is 12.
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If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is?
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If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is?.
If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of the equation X square - 8 x + k is equal to zero exceed the other by 4 value of k is?.
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