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If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ is
- a)5
- b)4
- c)3
- d)6
Correct answer is option 'D'. Can you explain this answer?
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If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, the...
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If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, the...
Solution:
Given quadratic equation:
kx(x + 2) + 6 = 0
To find the value of k:
Let's solve the quadratic equation and find the value of k.
Step 1: Rewrite the quadratic equation in standard form:
kx^2 + 2kx + 6 = 0
Step 2: Calculate the discriminant:
The discriminant (D) of a quadratic equation is given by the formula:
D = b^2 - 4ac
In our equation, a = k, b = 2k, and c = 6.
Substituting the values, we get:
D = (2k)^2 - 4(k)(6)
D = 4k^2 - 24k
Step 3: Determine the condition for equal roots:
For a quadratic equation to have equal roots, the discriminant should be equal to zero.
So, D = 0.
Step 4: Solve the equation D = 0:
4k^2 - 24k = 0
Dividing the equation by 4:
k^2 - 6k = 0
Factoring out k:
k(k - 6) = 0
Step 5: Find the values of k:
Setting each factor equal to zero:
k = 0 or k - 6 = 0
Solving for k:
k = 0 or k = 6
Conclusion:
The values of k that satisfy the condition for equal roots are k = 0 and k = 6.
However, the given options are a) 5, b) 4, c) 3, and d) 6.
Therefore, the correct answer is option 'D' (6).
Given quadratic equation:
kx(x + 2) + 6 = 0
To find the value of k:
Let's solve the quadratic equation and find the value of k.
Step 1: Rewrite the quadratic equation in standard form:
kx^2 + 2kx + 6 = 0
Step 2: Calculate the discriminant:
The discriminant (D) of a quadratic equation is given by the formula:
D = b^2 - 4ac
In our equation, a = k, b = 2k, and c = 6.
Substituting the values, we get:
D = (2k)^2 - 4(k)(6)
D = 4k^2 - 24k
Step 3: Determine the condition for equal roots:
For a quadratic equation to have equal roots, the discriminant should be equal to zero.
So, D = 0.
Step 4: Solve the equation D = 0:
4k^2 - 24k = 0
Dividing the equation by 4:
k^2 - 6k = 0
Factoring out k:
k(k - 6) = 0
Step 5: Find the values of k:
Setting each factor equal to zero:
k = 0 or k - 6 = 0
Solving for k:
k = 0 or k = 6
Conclusion:
The values of k that satisfy the condition for equal roots are k = 0 and k = 6.
However, the given options are a) 5, b) 4, c) 3, and d) 6.
Therefore, the correct answer is option 'D' (6).
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If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?
Question Description
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?.
If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quadratic equation kx(x – 2) + 6 = 0 has equal roots, then the value of ‘k’ isa)5b)4c)3d)6Correct answer is option 'D'. Can you explain this answer?.
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