Find the Least Positive Value of k for Which the Equation x² + kx + 4 = 0 Has Equal Roots

Question:

\( x^2 + kx + 4 = 0 \)

Find the least positive value of \(k\) for which the equation has equal roots.

Solution

For equal roots, the discriminant must be zero.

\( D=b^2-4ac=0 \)

Here,

\( a=1,\quad b=k,\quad c=4 \)

Therefore,

\( k^2-4(1)(4)=0 \)

\( k^2-16=0 \)

\( k^2=16 \)

\( k=\pm4 \)

Among these values, the least positive value is

\( k=4 \)

Answer

\( \boxed{k=4} \)