Question

Find the values of k for which the given quadratic equation has real and distinct roots:
$\left(i\right)k{x}^2+2x+1=0\left(ii\right)k{x}^2+6x+1=0$

Answer 1

For getting real and distinct roots the discriminant of the quadratic equation should be greater than zero.
Therefore,
D>0

Now,

Here a=k, b=2, c=1

Therefore, 4k<4
Hence, for k<1 the quadratic equation will have real and distinct roots.


Here a=k, b=6, c=1
Therefore, $D=6^2-4\times k\times 1$

= 36 - 4k > 0

So, 4k < 36

k < 9

Hence, for k < 9 the quadratic equation will have two real and distinct roots.