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

Answer: (B)

$\frac{25}{16}$

Answer 2

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 $k$:

$16k = 25 \implies k = \frac{25}{16}$