If one real root of the quadratic equation
Question:

If one real root of the quadratic equation $81 x^{2}+k x+256=0$ is cube of the other root, then a value of k is

  1. –81

  2. 100

  3. –300

  4. 144


Correct Option: , 3

Solution:

$81 x^{2}+k x+256=0 ; x=\alpha, \alpha^{3}$

$\Rightarrow \alpha^{4}=\frac{256}{81} \Rightarrow \alpha=\pm \frac{4}{3}$

Now $-\frac{\mathrm{k}}{81}=\alpha+\alpha^{3}=\pm \frac{100}{27}$

$\Rightarrow k=\pm 300$

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