If –4 is a root of the equation x² + px – 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k.

To find the value of k, we can use the fact that if a quadratic equation has equal roots, then its discriminant is equal to zero.

The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula Δ = b² - 4ac.

In this case, the quadratic equation x² + px + k = 0 has equal roots, so its discriminant is zero.

Substituting the values into the formula, we have (p)² - 4(1)(k) = 0.

Expanding the equation, we get p² - 4k = 0.

Since we know that -4 is a root of the equation x² + px – 4 = 0, we can substitute x = -4 into the equation to find the value of p.

(-4)² + p(-4) - 4 = 0.

Simplifying the equation, we have 16 - 4p - 4 = 0.

Combining like terms, we get 12 - 4p = 0.

Solving for p, we have p = 3.

Now, substituting p = 3 into the equation p² - 4k = 0, we can solve for k.

(3)² - 4k = 0.

Expanding the equation, we have 9 - 4k = 0.

Solving for k, we get k = 9/4.

Therefore, the value of k is 9/4.