Question

please solve it polynomial question

Answer 1

Hey!!

your answer is ----

firstly , we factorise x^2-3x+2

x^2-3x+2 = 0

=> x^2-2x-x+2 =0

=> x(x-2) - (x-2) = 0

=> (x-2)(x-1) = 0

=> x = 2 or 1


since , x^2 -3x +2 is a factor of
p(x) = x^4-px^2+q

so, when x = 2

then, p(2)=0

=> 2^4 - p×2^2 + q =0

=> 16 -4p + q = 0

=> 4p - q = 16 .. (1)

when, x = 1

then, p(1)=0

=> 1^4 - p×1^2+q =0

=> 1 -p +q =0

=> p - q = 1. ....(2)


subtract equation (1)&(2),we get

4p - q -(p - q) = 16 -1

=> 4p - q - p + q = 15

=> 3p = 15

=> p = 5

put this value in equation (2) , we get

p - q = 1

=> 5 - q = 1

=> q = 5-1 = 4

hence, p = 5 & q = 4

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