DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > The roots of the equation 2 a2x2- 2abx + b2= ...
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The roots of the equation 2 a2x2 - 2abx + 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?
Verified Answer
The roots of the equation 2 a2x2- 2abx + b2= 0 when a<0 and b>0 ...
We have, 2a2x2 - 2abx + b2 = 0
Discriminant, D = (-2ab)2 - 4(2a2)(b2)
= 4a2b2 - 8a2 b2 = - 4a2b2 < 0
Roots are always complex.
Discriminant, D = (-2ab)2 - 4(2a2)(b2)
= 4a2b2 - 8a2 b2 = - 4a2b2 < 0
Roots are always complex.
Most Upvoted Answer
The roots of the equation 2 a2x2- 2abx + b2= 0 when a<0 and b>0 ...
Explanation:
First, let's rewrite the given quadratic equation in the standard form:
2a^2x^2 - 2abx + b^2 = 0
Discriminant:
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.
For the given equation, the discriminant is (-2ab)^2 - 4(2a^2)(b^2) = 4a^2b^2 - 8a^2b^2 = -4a^2b^2.
Analysis:
1. If a < 0="" and="" b="" /> 0, then a^2 > 0 and b^2 > 0.
2. Since the discriminant is -4a^2b^2, it is always negative for a < 0="" and="" b="" /> 0.
3. A negative discriminant implies that the roots of the quadratic equation are complex conjugate.
Therefore, the roots of the equation 2a^2x^2 - 2abx + b^2 = 0, when a < 0="" and="" b="" /> 0, are always complex.
This analysis confirms that option 'C' (Always complex) is the correct answer.
First, let's rewrite the given quadratic equation in the standard form:
2a^2x^2 - 2abx + b^2 = 0
Discriminant:
The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.
For the given equation, the discriminant is (-2ab)^2 - 4(2a^2)(b^2) = 4a^2b^2 - 8a^2b^2 = -4a^2b^2.
Analysis:
1. If a < 0="" and="" b="" /> 0, then a^2 > 0 and b^2 > 0.
2. Since the discriminant is -4a^2b^2, it is always negative for a < 0="" and="" b="" /> 0.
3. A negative discriminant implies that the roots of the quadratic equation are complex conjugate.
Therefore, the roots of the equation 2a^2x^2 - 2abx + b^2 = 0, when a < 0="" and="" b="" /> 0, are always complex.
This analysis confirms that option 'C' (Always complex) is the correct answer.
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The roots of the equation 2 a2x2- 2abx + 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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