Question

In the following , determine the set of values of k for which the given quadratic equation has real roots:
(i) (ii) $2x^2+x+k=0$ (iii)

(iv) (v)

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 $2x^2+x+k=0$, and roots are real.

Then find the value of k.

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

As we know that

Putting the value of $a=2,b=1,c=k$
$D=1-8k$

The given equation will have real roots, if
$$\begin{gathered} D=1-8k\ge 0 \\ \Rightarrow 8k\le 1 \\ \Rightarrow k\le \frac{1}{8} \end{gathered}$$

Therefore, the value of $k\le \frac{1}{8}$.

(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

Therefore, the value of

(v) 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