A) \[(3,\,\,4)\]
B) \[(4,\,\,5)\]
C) \[(4,\,\,3)\]
D) \[(5,\,\,4)\]
Correct Answer: D
Solution :
Key Idea: If\[a{{x}^{2}}+bx+c\]is a factor of\[{{x}^{4}}+d{{x}^{2}}+e\], then the roots of the quadratic equation will satisfy the equation. Let \[f(x)={{x}^{2}}-3x+2=0\] \[\Rightarrow \] \[(x-2)(x-1)=0\] \[\Rightarrow \] \[x=1,\,\,2\] Since, \[{{x}^{2}}-3x+2\] be the factor of\[{{x}^{4}}-p{{x}^{2}}+q=0\]. \[\therefore \]The value of \[x\] will satisfy it. \[\Rightarrow \] \[1-p+q=0\]and\[16-4p+q=0\] \[\Rightarrow \] \[p=5,\,\,q=4\]
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