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Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots?
Most Upvoted Answer
Find the value of k for which the quadratic equation 9x^2-3k+k =0 has ...
For having equal roots discriminant=0
or,b^2-4AC=0
(-3k)^2-4(9)(k)=0
9k^2-36k=0
9k^2=36k
k=36k/9k
k=4
or,b^2-4AC=0
(-3k)^2-4(9)(k)=0
9k^2-36k=0
9k^2=36k
k=36k/9k
k=4
Community Answer
Find the value of k for which the quadratic equation 9x^2-3k+k =0 has ...
Finding the Value of k for Equal Roots in a Quadratic Equation:
To find the value of k for which the quadratic equation 9x^2-3k+k=0 has equal roots, we need to first determine the conditions for equal roots in a quadratic equation.
Condition for Equal Roots:
For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant (b^2 - 4ac) should be equal to zero.
Given Quadratic Equation:
9x^2 - 3kx + k = 0
Finding Discriminant:
In this case, a = 9, b = -3k, and c = k.
The discriminant is calculated as: (-3k)^2 - 4*9*k = 0
9k^2 - 36k = 0
k(9k - 36) = 0
Solving for k:
Setting k(9k - 36) = 0, we get two possible solutions:
1. k = 0
2. 9k - 36 = 0
9k = 36
k = 4
Conclusion:
Therefore, the value of k for which the quadratic equation 9x^2-3kx+k=0 has equal roots is k = 0 or k = 4. These values satisfy the condition of having a discriminant equal to zero, indicating equal roots for the quadratic equation.
To find the value of k for which the quadratic equation 9x^2-3k+k=0 has equal roots, we need to first determine the conditions for equal roots in a quadratic equation.
Condition for Equal Roots:
For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant (b^2 - 4ac) should be equal to zero.
Given Quadratic Equation:
9x^2 - 3kx + k = 0
Finding Discriminant:
In this case, a = 9, b = -3k, and c = k.
The discriminant is calculated as: (-3k)^2 - 4*9*k = 0
9k^2 - 36k = 0
k(9k - 36) = 0
Solving for k:
Setting k(9k - 36) = 0, we get two possible solutions:
1. k = 0
2. 9k - 36 = 0
9k = 36
k = 4
Conclusion:
Therefore, the value of k for which the quadratic equation 9x^2-3kx+k=0 has equal roots is k = 0 or k = 4. These values satisfy the condition of having a discriminant equal to zero, indicating equal roots for the quadratic equation.
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Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots?.
Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k for which the quadratic equation 9x^2-3k+k =0 has equal roots?.
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