if two zeros of cubic polynomial p x is equals to x cube + b x square + c x + d are 0 , then c=d=0 true or false

Question

if two zeros of cubic polynomial p x is equals to x cube + b x square + c x + d are 0 , then c=d=0 true or false​

Savannah · Answer

Answer:   No it's false   Step-by-step explanation:   actually the given question also consist zeros 1 and -1 actually it is not given in question given by you    Given   p(x) =  {x}^{3}  + bx ^{2}  + cx + d    Substituting 1 as the root of p(x) we get as  follows   p(1) = 0    p( - 1) = 0   hence substituting these values in starting equation we get as follows   p(1) =  ({1})^{3}  + b ({1})^{2}  + c(1) + d = 0    p(1) = 1 + b + c + d = 0   let it be equation (1)  now taking -1 as other root   p( - 1) =  ({ - 1})^{3}  + b ({ - 1})^{2}  + c( - 1) + d = 0    p( - 1) = ( - 1) + b - c + d = 0   =>consider it as equation (2)        =>now by considering equation (1) and (2)    =>We get as follows     p(1) =  0   p( - 1) = 0    p(1) + p( - 1) = 0    (1 + b + c + d) = 0    ( - 1 + b - c + d )= 0    adding them we get   2b + 2d = 0    b + d = 0   since b+d=0    =>from equation (1) we get    =>c=-1     =>since we got c=-1    =>c≠d    =>so the given statement is false    =>the true statement is    =>c=d=-1    = as b+d=0     B  y trail and error method      =>b can be any positive or negative integer    =>d can be any positive or negative integer    =>as c=-1 c must be not equal to o    =>hence c≠d≠0

Ayla · Answer

Answer:   duzuzddzusddusudzzdudsudsufzufzsidisf

Piper

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