Question

If one root of the equation x2-x-k=0 be square of the other then k os equal to

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value of k is $2-\sqrt{5}$

1) The given equation is x^2 - x - k = 0.

2) a= 1, b = -1, c= -k for the given equation.

3) Let one root be z, then other root would be z^2.

4) Using quadratic formula, D = b^2 - 4ac = 1+4k.

5) z=(1+  $\sqrt{1+4k}$)/2 and z^2 = (1-$\sqrt{1+4k}$)/2.

6) Solving these two equations in two variables k and z gives value of k as 2 - $\sqrt{5}$ or -0.23.

7) The roots of the equation would be $\frac{\sqrt{5}-1 }{2}$ and $\frac{3- \sqrt{5} }{2}$