• # question_answer If ${{x}^{2}}+px+q=0$ is the quadratic equation whose roots are a - 2 and b - 2 where a and b are the roots of ${{x}^{2}}-3x+1=0$, then [Kerala (Engg.) 2002] A) $p=1,\,q=5$  B) $p=1,\,q=-5$ C) $p=-1,\,\,q=1$ D) None of these

Correct Answer: D

Solution :

$a+b=3$, $ab=1$ and$-p=a-2+b-2$,$q=(a-2)(b-2)$ Þ $-p=a+b-4$, $q=ab-2(a+b)+4$ $\Rightarrow -p=3-4$ and$q=1-2(3)+4$ Þ $(p,\,q)=(1,\,-1)$.

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