Question

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots. 

Answer 1

The given quadric equation is x² + kx + 4 = 0, and roots are real.

Then find the value of k.

Here,

a = 1, b = k and c = 4

As we know that D = b² − 4ac

Putting the value of a = 1, b = k and c = 4

= k² − 4 × (1) × (4)

= k² − 16

The given equation will have real and equal roots, if D = 0

k² − 16 = 0

Now factorizing of the above equation

k² − 16 = 0

k² = 16

`k=sqrt16`

k = ± 4

Now according to question, the value of k is positive.

Therefore, the value of k = 4