Question

Determine the set of values of k for which the following quadratic equation have real roots:
(i) (ii)

(iii) (iv)

Answer 1

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

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real roots, if

Therefore, the value of

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

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real roots, if

Therefore, the value of

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

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real roots, if

Therefore, the value of

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

Then find the value of k.

Here,

As we know that

Putting the value of

The given equation will have real roots, if

Since left hand side is always positive. So

Therefore, the value of