#### Question

Find the least positive value of *k* for which the equation *x*^{2} + *kx* + 4 = 0 has real roots.

#### Solution

The given quadric equation is *x*^{2} + *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 = b^{2} - 4ac

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

= k^{2} - 4 x (1) x (4)

= k^{2} - 16

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

k^{2} - 16 = 0

Now factorizing of the above equation

k^{2} - 16 = 0

k^{2} = 16

`k=sqrt16`

k = ± 4

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

Therefore, the value of k = 4

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Least Positive Value Of K For Which the Equation X2 + Kx + 4 = 0 Has Real Roots. Concept: Nature of Roots.