4. Find the values of k for which the following equations have real and equal roots (iii) \[\left( \mathbf{k}\text{ }+\text{ }\mathbf{1} \right){{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{2}\left( \mathbf{k}\text{ }\text{ }\mathbf{1} \right)\mathbf{x}\text{ }+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}\]

Home » 4. Find the values of k for which the following equations have real and equal roots (iii)

4. Find the values of k for which the following equations have real and equal roots (iii)

$\left( \mathbf{k}\text{ }+\text{ }\mathbf{1} \right){{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{2}\left( \mathbf{k}\text{ }\text{ }\mathbf{1} \right)\mathbf{x}\text{ }+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}$

4. Find the values of k for which the following equations have real and equal roots (iii)

$\left( \mathbf{k}\text{ }+\text{ }\mathbf{1} \right){{\mathbf{x}}^{\mathbf{2}}}~\text{ }\mathbf{2}\left( \mathbf{k}\text{ }\text{ }\mathbf{1} \right)\mathbf{x}\text{ }+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}$

Solution:

Given :

$\left( k\text{ }+\text{ }1 \right){{x}^{2}}~\text{ }2\left( k\text{ }\text{ }1 \right)x\text{ }+\text{ }1\text{ }=\text{ }0$

It’s of the form of

$a{{x}^{2~}}+\text{ }bx\text{ }+\text{ }c\text{ }=\text{ }0$

a = $(k + 1)$ , b = $-2(k - 1)$ , c = $1$

For the given quadratic equation to have real roots

$D\text{ }=\text{ }{{b}^{2~}}\text{ }4ac\text{ }=\text{ }0$

$D\text{ }=\text{ }{{\left( -2\left( k\text{ }\text{ }1 \right) \right)}^{2}}~\text{ }4\left( 1 \right)\left( k\text{ }+\text{ }1 \right)\text{ }=\text{ }0$