# Find the value of k for which the given quadratic equation has real and distinct roots and also find the roots. k x^2 +2x+1=0.

$\begin{array}{l}\text{Given.}\\ kx^2+2x+1=0\ \text{, It roots are real and distinc.}\\ \text{As we know,}\ ax^2+bx+c=0\ ,\ x=\frac{\left(-b+\sqrt{b^2-4ac}\right)}{2a}\\ \text{So, roots of given equcation}\\ x=\frac{\left(-2+\sqrt{2^2-4k}\right)}{2k}\\ \text{For real roots,}\ D>0\ ,\ \\ 2^2-4k>0\ \\ \Rightarrow k<1\\ \text{So, all values of}\ k<1,\ \text{roots are real and distinct.}\end{array}$

### Preparation Products

##### Knockout NEET May 2023 (Easy Installments)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 5499/-
##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-