The volume of the cuboid having combined equations of opposite faces as x2−3x−4=0,y2−5y+6=0 and z2+6z+8=0 is

we have x2−3x−4=0⇒    (x−4)(x+1)=0⇒     x=4,x=−1Distance between two parallel planes (parallel to yz-plane) is 5 units.⇒ (y−2)(y−3)=0⇒ y=2,y=3we have y2−5y+6=0Distance between two parallel planes (parallel to xz-plane) is I unit. we have z2+6z+8=0⇒ (z+2)(z+4)=0⇒ z=−2,z=−4Distance between two parallel planes (parallel to xxy-plane) is 2 unit. So, volume of cuboid is 5 x 1 x 2: 10 cu. units.