Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring.
(iii) 
Solution:
Given,
It’s of the form of 
Where, 
For the given quadratic equation to have real roots 
⇒ 
⇒ 
⇒ 
and 
⇒
The value of 
should be greater than or equal to 
to have real roots.
(iv) 
Solution:
Given,
It can be rewritten as,
It’s of the form of
Where, 
For the given quadratic equation to have real roots
⇒ 
⇒ 
⇒ and 
⇒
The value of should be greater than or equal to 
to have real roots.
![\[\begin{array}{l} \square \vec{r}=(\hat{i}+\hat{j})+\lambda(2 \hat{i}-\hat{j}+\hat{k}) \\ \vec{r}=(2 \hat{i}+\hat{j}-\hat{k})+\mu(3 \hat{i}-5 \hat{j}+2 \hat{k}) \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2f8ab5b81e582387cb9ae472791476e4_l3.png "Rendered by QuickLaTeX.com")
![\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{-2}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5a91864ba7e1e0ed1b5d273d822f5e5_l3.png "Rendered by QuickLaTeX.com")
(b) ![\left[\mathrm{Pd}(\mathrm{CN})_{4}\right]^{2-}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ffda616d3dbe7dc8925722e87005924e_l3.png "Rendered by QuickLaTeX.com")
(c) ![\left[\mathrm{PdCl}_{4}\right]^{2-}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-90cc6a4f4d42dee46e06d6f8ed516b7a_l3.png "Rendered by QuickLaTeX.com")
(d) ![\left[\mathrm{NiCl}_{4}\right]^{2}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-149ee5c95bd9cfcc4405704fba2e1bab_l3.png "Rendered by QuickLaTeX.com")
(d) all of these