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The roots of the equation 2a2x2 – 2abx + b2 = 0 When a < 0 and b > 0 are:

The roots of the equation 2a2x2 – 2abx + b2 = 0 When a < 0 and b > 0 are: Correct Answer Always complex

Concept:

Let us consider the standard form of a quadratic equation, ax2 + bx + c = 0

Where a, b and c are constants with a ≠ 0

  • Discriminant = D = b2 – 4ac

 

Calculation:

Given that: 2a2x2 – 2abx + b2 = 0

Let a quadratic equation Ax2 + Bx + C = 0

Here, A = 2 a2, B = -2 ab and C = b2

Now,

Discriminant (D) = B2 – 4 A C = (-2 ab) 2 – 4 × 2 a2 × b2

D = 4 a2b2 – 8 a2b2 = -4 a2b2 = -4 (ab) 2

We know that a square will always be positive,

So, (ab)2 > 0

Hence, D < 0

Since the discriminant of the given quadratic equation is less than zero, the roots of the given equation are always complex. Hence option 3 is correct.

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