Question

If the roots of quadratic equation \(4x^2 - 5x + k = 0\) are real and equal, then value of \(k\) is:

• A. \(\frac{5}{4}\)
• B. \(\frac{25}{16}\)
• C. \(-\frac{5}{4}\)
• D. \(-\frac{25}{16}\)

Answer 1

The Correct Option is B

For a quadratic equation \(ax^2 + bx + c = 0\), the condition for real and equal roots is:

\[ \Delta = b^2 - 4ac = 0 \]

For the given quadratic equation \(4x^2 - 5x + k = 0\), we have:

• \(a = 4\)
• \(b = -5\)
• \(c = k\)

Substitute the values into the discriminant formula:

\[ \Delta = (-5)^2 - 4(4)(k) = 0 \]

\[ 25 - 16k = 0 \]

Solve for \(k\):

\[ 16k = 25 \implies k = \frac{25}{16} \]