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The roots of the equation a2x2 - 2 abx + b2 = 0 when a < 0 and b > 0 are:
- a)Sometimes complex
- b)Always irrational
- c)Always complex
- d)Always real
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The roots of the equation a2x2 - 2 abx + b2 = 0 when a < 0 and b &g...
We have, 2a2 x2 - 2abx + b2 = 0
Discriminent, D=( - 2ab)2 - 4 (2a2) (b2)
= 4a2b2 - 8 a2b2 = - 4 a2b2 < 0
Roots are always complex.
Discriminent, D=( - 2ab)2 - 4 (2a2) (b2)
= 4a2b2 - 8 a2b2 = - 4 a2b2 < 0
Roots are always complex.
Most Upvoted Answer
The roots of the equation a2x2 - 2 abx + b2 = 0 when a < 0 and b &g...
Complex Roots of the Equation a^2x^2 - 2abx + b^2 = 0
When solving the quadratic equation a^2x^2 - 2abx + b^2 = 0, where a < 0="" and="" b="" /> 0, we can analyze the nature of the roots.
Explanation:
Discriminant Method:
- The discriminant of the quadratic equation ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac.
- For the equation a^2x^2 - 2abx + b^2 = 0, the discriminant is (-2ab)^2 - 4(a^2)(b^2) = 4a^2b^2 - 4a^2b^2 = 0.
- When the discriminant is equal to zero, the equation has equal roots, which are always complex.
Conclusion:
- In this case, since the discriminant is zero, the roots of the equation a^2x^2 - 2abx + b^2 = 0 when a < 0="" and="" b="" /> 0 are always complex.
- Therefore, option 'C' - Always complex, is the correct answer for this question.
This explanation highlights the nature of the roots of the given quadratic equation based on the values of a and b, providing a clear understanding of why the roots are always complex in this scenario.
When solving the quadratic equation a^2x^2 - 2abx + b^2 = 0, where a < 0="" and="" b="" /> 0, we can analyze the nature of the roots.
Explanation:
Discriminant Method:
- The discriminant of the quadratic equation ax^2 + bx + c = 0 is given by Δ = b^2 - 4ac.
- For the equation a^2x^2 - 2abx + b^2 = 0, the discriminant is (-2ab)^2 - 4(a^2)(b^2) = 4a^2b^2 - 4a^2b^2 = 0.
- When the discriminant is equal to zero, the equation has equal roots, which are always complex.
Conclusion:
- In this case, since the discriminant is zero, the roots of the equation a^2x^2 - 2abx + b^2 = 0 when a < 0="" and="" b="" /> 0 are always complex.
- Therefore, option 'C' - Always complex, is the correct answer for this question.
This explanation highlights the nature of the roots of the given quadratic equation based on the values of a and b, providing a clear understanding of why the roots are always complex in this scenario.
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The roots of the equation a2x2 - 2 abx + b2 = 0 when a < 0 and b > 0 are:a)Sometimes complexb)Always irrationalc)Always complexd)Always realCorrect answer is option 'C'. Can you explain this answer?
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