If –3 is a root of the quadratic equation 2x² + px – 15 = 0, while the quadratic equation x² – 4px + k = 0 has equal roots, find the value of k.

Given –3 is a root of the quadratic equation 2x² + px – 15 = 0.

So, 2(-3)² + p (-3) – 15 = 0

⇒ 18 – 3p – 15 = 0

⇒ 3 – 3p = 0

⇒ 3 = 3p

∴ p = 1

Also given, the quadratic equation x² – 4px + k = 0 has equal roots.

Substituting value of p in above equation, we get

⇒ x² – 4(1)x + k = 0

⇒ x² – 4x + k = 0

We know that a quadratic equation ax² + bx + c = 0 has two equal roots (i.e., coincident roots), if b² – 4ac = 0.

Here, a = 1; b = -4; c = k

So, (-4)² – 4(1) (k) = 0

⇒ 16 – 4k = 0

⇒ 4k = 16

∴ k = 4

Answer: The value of k is 4.