Question

For what values of k, the roots of the equation x²+4x+k=0 are real

Answer 1

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k ≤ 4

step-by-step explanation:

Given,

quadratic equation is

x²+4x+k=0

where,

a = 1

b = 4

c = k

Now,

we know that,

for real roots of a quadratic equation,

Descriminant, D ≥ 0

but,

D = b² - 4ac

=> b² - 4ac ≥ 0

=> 4² - 4 × 1 × k ≥ 0

=> 16 - 4k ≥ 0

adding 4k on both sides,

we get,

=> 4k ≤ 16

Dividing bith sides with 4,

we get,

=> 4k/4 ≤ 16/4

=> k ≤ 4

Hence,

for real roots,

k ≤ 4