The roots of the quadratic equation x2-2a-b x-2a2-b2-0q-b are

The correct option is C imaginaryx^2 2(a+b)x+2(a^2+b^2)=0 nbsp; Δ=4(a+b)^2 8(a^2+b^2) =4a^2+4b^2+8ab 8a^2 8b^2 = 4a^2 4b^2+8ab = 4(a b)^2 lt;0 Hence, roots ...

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Standard XIII

Mathematics

Nature of Roots

The roots of ...

Question

The roots of the quadratic equation $x^{2} - 2 (a + b) x + 2 (a^{2} + b^{2}) = 0 (a \neq b)$ are

real and distinct

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rational

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real and equal

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imaginary

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Solution

The correct option is D imaginary
$x^{2} - 2 (a + b) x + 2 (a^{2} + b^{2}) = 0$
$Δ = 4 (a + b)^{2} - 8 (a^{2} + b^{2})$
$= 4 a^{2} + 4 b^{2} + 8 a b - 8 a^{2} - 8 b^{2}$
$= - 4 a^{2} - 4 b^{2} + 8 a b$
$= - 4 (a - b)^{2} < 0$
Hence, roots are imaginary.

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The roots of the quadratic equation x2−2(a+b)x+2(a2+b2)=0 (a≠b) are

The correct option is D imaginaryx2−2(a+b)x+2(a2+b2)=0 Δ=4(a+b)2−8(a2+b2) =4a2+4b2+8ab−8a2−8b2 =−4a2−4b2+8ab =−4(a−b)2<0 Hence, roots are imaginary.

The roots of the quadratic equation $x^{2} - 2 (a + b) x + 2 (a^{2} + b^{2}) = 0 (a \neq b)$ are

The correct option is D imaginary
$x^{2} - 2 (a + b) x + 2 (a^{2} + b^{2}) = 0$
$Δ = 4 (a + b)^{2} - 8 (a^{2} + b^{2})$
$= 4 a^{2} + 4 b^{2} + 8 a b - 8 a^{2} - 8 b^{2}$
$= - 4 a^{2} - 4 b^{2} + 8 a b$
$= - 4 (a - b)^{2} < 0$
Hence, roots are imaginary.