verify that 4,-1,-1/4 are the zeroes of cubic polynomial 4x³-11x²-19x-4 and check the relationship between zeroes and coefficients
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Verification
p(4)= 4(4)^3 -11(4)^2 -19(4)-4
=4(64)-11(6)-76-4
=256-176-76-4 =0
p(-1)=4(-1)^3-11(-1)^2-19(-1)-4
=-4-11+19-4 =0
p(-1/4)=4(-1/4)^3 -11(-1/4)^2-19(-1/4)-4
=4(-1/64)-11(-1/16)-19(-1/4)-4
= -4/64 -11/16 +19/4 -4
= -4-44+304-256/64. [Taking LCM]
=0/64=0
p(4)= 4(4)^3 -11(4)^2 -19(4)-4
=4(64)-11(6)-76-4
=256-176-76-4 =0
p(-1)=4(-1)^3-11(-1)^2-19(-1)-4
=-4-11+19-4 =0
p(-1/4)=4(-1/4)^3 -11(-1/4)^2-19(-1/4)-4
=4(-1/64)-11(-1/16)-19(-1/4)-4
= -4/64 -11/16 +19/4 -4
= -4-44+304-256/64. [Taking LCM]
=0/64=0
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