Question:
If the equation $x^{2}+4 x+k=0$ has real and distinct roots, then
(a) $k<4$
(b) $k>4$
(c) $k \geq 4$
(d) $k \leq 4$
Solution:
The given quadric equation is $x^{2}+4 x+k=0$, and roots are real and distinct.
Then find the value of k.
Here, $a=1, b=4$ and, $c=k$
As we know that $D=b^{2}-4 a c$
Putting the value of $a=1, b=4$ and,$c=k$
$=(4)^{2}-4 \times 1 \times k$
$=16-4 k$
The given equation will have real and distinct roots, if $D>0$
$16-4 k>0$
$4 k<16$
$k<\frac{16}{4}$
$<4$
Therefore, the value of $k<4$
Thus, the correct answer is (a)