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If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:?
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If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value...
Given Equation:
(x-1)(x-5) = k
Condition Given:
The roots of the equation differ by 2.
Understanding the Roots:
The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the formula x = (-b ± √(b^2 - 4ac))/2a.
In this case, the roots of the given equation (x-1)(x-5) = k can be found by setting it equal to zero and solving for x.
Finding the Roots:
(x-1)(x-5) = k
Expanding,
x^2 - 5x - x + 5 = k
x^2 - 6x + 5 = k
Setting it equal to zero,
x^2 - 6x + 5 - k = 0
Using the Quadratic Formula:
The roots of the equation x^2 - 6x + 5 - k = 0 will be x = (6 ± √(36 - 4(1)(5-k)))/2
Applying the Condition:
The roots differ by 2, so the discriminant (√(36 - 4(1)(5-k))) should equal 2.
Solving for k:
36 - 4(5-k) = 4
36 - 20 + 4k = 4
16 + 4k = 4
4k = -12
k = -3
Therefore, the value of k is -3 for the roots of the equation (x-1)(x-5) = k to differ by 2.
(x-1)(x-5) = k
Condition Given:
The roots of the equation differ by 2.
Understanding the Roots:
The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the formula x = (-b ± √(b^2 - 4ac))/2a.
In this case, the roots of the given equation (x-1)(x-5) = k can be found by setting it equal to zero and solving for x.
Finding the Roots:
(x-1)(x-5) = k
Expanding,
x^2 - 5x - x + 5 = k
x^2 - 6x + 5 = k
Setting it equal to zero,
x^2 - 6x + 5 - k = 0
Using the Quadratic Formula:
The roots of the equation x^2 - 6x + 5 - k = 0 will be x = (6 ± √(36 - 4(1)(5-k)))/2
Applying the Condition:
The roots differ by 2, so the discriminant (√(36 - 4(1)(5-k))) should equal 2.
Solving for k:
36 - 4(5-k) = 4
36 - 20 + 4k = 4
16 + 4k = 4
4k = -12
k = -3
Therefore, the value of k is -3 for the roots of the equation (x-1)(x-5) = k to differ by 2.
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If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:?
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If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:?.
If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of equation (x-1)( x-5 ) k= 0 differ by 2 then the value of k is:?.
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