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If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is?
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If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value...
To determine the value of m for which the roots of the equation 2x² + 8x - m³ = 0 are equal, we need to apply the concept of the discriminant from quadratic equations.
Understanding the Discriminant
- The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula: D = b² - 4ac.
- For the roots to be equal, the discriminant must be equal to zero (D = 0).
Applying the Formula
- Here, a = 2, b = 8, and c = -m³.
- Substitute these values into the discriminant formula:
D = 8² - 4(2)(-m³)
- Simplifying this gives:
D = 64 + 8m³.
Setting the Discriminant to Zero
- For equal roots, set the discriminant equal to zero:
64 + 8m³ = 0.
- Rearranging this equation leads to:
8m³ = -64.
Solving for m
- Dividing both sides by 8 yields:
m³ = -8.
- Taking the cube root of both sides gives us:
m = -2.
Conclusion
- The value of m for which the roots of the equation 2x² + 8x - m³ = 0 are equal is m = -2.
Understanding the Discriminant
- The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula: D = b² - 4ac.
- For the roots to be equal, the discriminant must be equal to zero (D = 0).
Applying the Formula
- Here, a = 2, b = 8, and c = -m³.
- Substitute these values into the discriminant formula:
D = 8² - 4(2)(-m³)
- Simplifying this gives:
D = 64 + 8m³.
Setting the Discriminant to Zero
- For equal roots, set the discriminant equal to zero:
64 + 8m³ = 0.
- Rearranging this equation leads to:
8m³ = -64.
Solving for m
- Dividing both sides by 8 yields:
m³ = -8.
- Taking the cube root of both sides gives us:
m = -2.
Conclusion
- The value of m for which the roots of the equation 2x² + 8x - m³ = 0 are equal is m = -2.
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If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is?
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If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m 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 the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is?.
If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m 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 the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of the equation 2x ^ 2 + 8x - m ^ 3 = 0a equal then value of m is?.
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