A) \[-2\] and \[5\]
B) \[5\] and \[25\]
C) \[10\] and \[20\]
D) \[6\] and \[25\]
Correct Answer: D
Solution :
Let the other factor be \[{{x}^{2}}+ax+b\]. We have \[({{x}^{2}}+2x+5)\,\,({{x}^{2}}+ax+b)\] \[={{x}^{4}}+p{{x}^{2}}+q\] \[{{x}^{4}}+(2+a){{x}^{3}}+(2a+b+5){{x}^{2}}+\] \[(5a+2b)x+5b={{x}^{4}}+p{{x}^{2}}+q\] Comparing the coefficients of corresponding terms, we get \[2a+b+5=p\] ......(1) \[5b=q\] ......(2) \[2+a=0\] \[\Rightarrow \] \[a=-2\] \[5a+2b=0\] \[\Rightarrow \] \[b=5\] \[\therefore \] \[p=2a+b+5=2(-2)+5+5=6\] \[q=5b=5(5)=25\]
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