(A) Given the quadratic equation: $16x^2-10x+1=0$ Factorizing the equation: $16x^2-8x-2x+1=0$ $\Rightarrow 8x(2x-1)-1(2x-1)=0$ $\Rightarrow (8x-1)(2x-

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(A) Given the quadratic equation: $16x^2-10x+1=0$ Factorizing the equation: $16x^2-8x-2x+1=0$ $\Rightarrow 8x(2x-1)-1(2x-1)=0$ $\Rightarrow (8x-1)(2x-1)=0$ The roots are $x_1 = \frac{1}{8}$ and $x_2 = \frac{1}{2}$ The sum of the fourth powers of the roots is: $(\frac{1}{8})^4 + (\frac{1}{2})^4 = \frac{1}{4096} + \frac{1}{16}$ $= \frac{1 + 256}{4096} = \frac{257}{4096}$

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The sum of the fourth powers of the roots of the equation $16x^2-10x+1=0$ is

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A
$\frac{257}{4096}$
B
$\frac{257}{2048}$
C
$\frac{257}{1024}$
D
$\frac{257}{512}$

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