Question

Find the values of k for which the given quadratic equation has real and distinct roots:

(a) kx² + 2x + 1 = 0
(b) kx² + 6x + 1 = 0
(c) x² − kx + 9 = 0

Answer 1

(i) The given quadric equation is , and roots are real and distinct

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real and distinct roots, if

Now factorizing of the above equation

Now according to question, the value of k less than 1

Therefore, the value of

(ii) The given quadric equation is , and roots are real and distinct.

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real and distinct roots, if

Now factorizing of the above equation

Now according to question, the value of k less than 9

Therefore, the value of

(iii) The given quadric equation is , and roots are real and distinct

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real and distinct roots, if

Now factorizing of the above equation

Therefore, the value of