Given x = (-1, 5) for the equation x2+kx−5=0x^{2} + kx - 5 = 0x2+kx−5=0
x=−1 ⟹ x+1=0x = -1 \implies x + 1 = 0x=−1⟹x+1=0; x=5 ⟹ x−5=0x = 5 \implies x - 5 = 0x=5⟹x−5=0
(x+1)(x−5)=0(x + 1)(x - 5) = 0(x+1)(x−5)=0, expanding,
x2−5x+x−5=0∴x2−4x−5=0x^{2} - 5x + x - 5 = 0 \therefore x^{2} - 4x - 5 = 0x2−5x+x−5=0∴x2−4x−5=0
∴\therefore∴ k = -4.
