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Determine the Nature of the Roots of the Following Quadratic Equation: 2(A2 + B2)X2 + 2(A + B)X + 1 = 0 - Mathematics

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Question

Determine the nature of the roots of the following quadratic equation:

2(a2 + b2)x2 + 2(a + b)x + 1 = 0

Solution

The given equation is

2(a2 + b2)x2 + 2(a + b)x + 1 = 0

The given equation is in the form of ax2 + bx + c = 0

where a = 2(a2 + b2), b = 2(a + b), c = 1

Therefore the discriminant

D = b2 - 4ac

= (2(a + b))2 - 4 x (2(a2 + b2)) x (1)

= 4(a + b)2 - 8a2 - 8b2

= 4(a2 + b2 + 2ab) - 8a2 - 8b2

= 4a2 + 4b2 + 8ab - 8a2 - 8b2

= 8ab - 4a2 - 4b2

∵ D < 0,

∴ The roots of the given equation are not real.

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 15.3 | Page no. 42
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 15.3 | Page no. 42
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Solution Determine the Nature of the Roots of the Following Quadratic Equation: 2(A2 + B2)X2 + 2(A + B)X + 1 = 0 Concept: Nature of Roots.
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