Question

For what value of k the quadratic equation x2+4x+k=0 has real rootss...

Answer 1

Answer:

$\bold\red{k≤4}$

Step-by-step explanation:

Given,

a quadratic equation,

$\bold{ {x}^{2} + 4x + k = 0}$

Now,

Comparing this equation with general form,

$\bold{a {x}^{2} + bx + c = 0}$

We get,

a = 1

b = 4

c = k

Now,

for the real roots of a quadratic equation,

Discriminant, D ≥ 0

But,

$\bold{D={b}^{2}-4ac}\\\\=>D={4}^{2}-4×1×k\\\\=>D=16-4k$

Now,

For real roots,

D ≥ 0

=> 16 - 4k ≥ 0

=> 4k ≤ 16

Hence, k ≤ 4