(i) Find the value of k for which x=1 is a root of the equation `x^(2)+kx+3=0.` Also, find the other root. (ii) Find the values of a and b for which `

Correct Answer - (i) `(729)^(1/3), root(3)(729)` (ii) `(1990)^(1/5), root(5)(1990)` (iii) `(2001)^(1/2), sqrt(2001)` (iv) `(777)^(1/7), root(7)(777)`

Correct Answer - (i) `15/4` (ii) `50/7`

Correct Answer - `root(9)(5),root(6)(9),root(3)(7)`

Correct Answer - local max. value is 19 at x = 1 and local min. value is 15 at x = 3

Correct Answer - local max. value is 68 at x = 1 and local min. values are `-1647 " at " x = -6 and -316 " at " x...

Correct Answer - (i) `k=0" or "k=1" "(ii)" "k=2`

Correct Answer - `k=(49)/(28)`

A) same l value and same n value

Correct option is B) \(\left(\mathrm{I}_{0} / \sqrt{2}, \mathrm{~V}_{0} / \sqrt{2}\right)\)

In the equation, Putting \(x=\frac{1}{\sqrt{3}}\) \(=px²+(\sqrt{3}-\sqrt{2})x+1=0\\=p(\frac{1}{\sqrt{3}})^{2}+(\sqrt{3}-\sqrt{2})\frac{1}{\sqrt{3}}+1=0\\=\frac{p}{3}+1-\frac{\sqrt{2}}{\sqrt{3}}+1=0\\ =\frac{p}{3}=\frac{\sqrt{2}}{\sqrt{3}}\\=p=\sqrt{2}×\sqrt{3}=\sqrt{6}\)