Question

If the equation x² + 4x + k = 0 has real and distinct roots, then
A. k < 4
B. k > 4
C. k ≥ 4
D. k ≤ 4

Answer 1

The value of k in the equation x² + 4x + k = 0 is given as k < 4. Hence, option (A) is the correct answer.

• It is given that the equation has real and distinct roots.

A quadratic equation can have real and distinct roots if the following condition is satisfied :

Discriminant > 0

• Now, discriminant of an equation is given as :

D = b² - 4ac,

where a is the coefficient of x²,

b is the coefficient of x,

and c is the constant in the equation.

• Therefore, for the given equation, a = 1, b = 4, c = k

∴  b² - 4ac > 0

=> 4² - 4.1.k > 0

=> 16 - 4k > 0

=> 16 > 4k

=> 4k < 16

=> k < 16 / 4

=> k < 4

∴   The value of k is less than 4 (option A).