If the equation x2 + 4x + k = 0 has real and distinct roots, then


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) $k \leq 4$


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 $D>0$

$16-4 k>0$

$4 k<16$



Therefore, the value of $k<4$

Thus, the correct answer is (a)


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