Question

If -2 is a root of the quadratic equation x2 - px + 4 = 0 and x2 + px – k=0 has equal roots, then the value of k is
A) -4 (B) 10 (C) 4 (D) -2​

Answer 1

$x^{2} -px+4=0\\\\if -2 is a root of the equation\\\\(-2)^{2} - p(-2)+4=0\\4+2p+4=0\\2p+8=0\\2p=-8\\p=-4$

replacing value of p in the other equation

$x^{2} -4x-k=0\\\\since the equation has equal roots\\\\D=0\\b^{2} -4ac = 0\\(-4)^{2} -4(1)(k)=0\\16-4k=0\\4k=16\\\\k=4$

therefore (c) 4  is the correct answer