1.

equal to ?1. 10242. 2563. 644. 16

Answer» Correct Answer - Option 2 : 256

Concept:

Consider a quadratic equation: ax2 + bx + c = 0.

Let, α and β are the roots.

  • Sum of roots = α + β = -b/a
  • Product of the roots = α × β = c/a

 

Calculation:

Given quadratic equation:  x2 + 6x + 4 = 0

Let  α and β are roots, then 

α + β = -6,  αβ = 4

Now,\(\frac{\alpha ^4+\beta ^4}{\alpha ^{-4}+\beta ^{-4}}\)= \(\frac{\alpha ^4+\beta ^4}{\frac {1}{\alpha ^{4}}+\frac{1}{\beta ^{4}}}\)

= \(\frac{\alpha ^4+\beta ^4}{\frac {(\alpha ^4+\beta ^4)}{\alpha^4 \beta^4 }}\)

= (αβ)4

= (4)4

= 256

Hence, option (2) is correct.


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