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The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, is
a)4
b)+- 4
c)-4
d)0
kindly explain the solution?
a)4
b)+- 4
c)-4
d)0
kindly explain the solution?
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The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has eq...
Understanding Equal Roots in Quadratic Equations
In a quadratic equation of the form ax² + bx + c = 0, equal roots occur when the discriminant (D) is zero. The discriminant is calculated using the formula:
D = b² - 4ac
For the given quadratic equation:
2x² + kx + 2 = 0
Here, a = 2, b = k, and c = 2.
Step 1: Set Up the Discriminant
To find the value of k for which the roots are equal, we set the discriminant to zero:
D = k² - 4(2)(2) = 0
This simplifies to:
k² - 16 = 0
Step 2: Solving for k
Now, we solve the equation:
k² = 16
Taking the square root of both sides:
k = ±4
Conclusion
Thus, the values of k for which the quadratic equation has equal roots are:
Therefore, the correct options are a) 4 and b) ±4.
In a quadratic equation of the form ax² + bx + c = 0, equal roots occur when the discriminant (D) is zero. The discriminant is calculated using the formula:
D = b² - 4ac
For the given quadratic equation:
2x² + kx + 2 = 0
Here, a = 2, b = k, and c = 2.
Step 1: Set Up the Discriminant
To find the value of k for which the roots are equal, we set the discriminant to zero:
D = k² - 4(2)(2) = 0
This simplifies to:
k² - 16 = 0
Step 2: Solving for k
Now, we solve the equation:
k² = 16
Taking the square root of both sides:
k = ±4
Conclusion
Thus, the values of k for which the quadratic equation has equal roots are:
- k = 4
- k = -4
Therefore, the correct options are a) 4 and b) ±4.
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The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution?
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The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution? 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 The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution?.
The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution? 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 The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value(s) of k for which quadratic equation 2x² + kx + 2 = 0 has equal roots, isa)4b)+- 4c)-4d)0kindly explain the solution?.
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